CFA Institute Research Objectivity Standards: research report

• CFA Institute Research Objectivity Standards recommend that firms provide full research reports on the subject companies discussed to members of the audience at a reasonable price.
• At a minimum, the covered employee should disclose whether a written research report is available to members of the audience who are not clients of the firm, the approximate cost, and how a listener might acquire the report.
• Firms should make copies of the full research report available for purchase or review; for example via the firm's website.

Withholding Tax

The standard approach is that withholding is applied to the dividend income only. Not to the capital gain.

Net Income Breakeven Point

Net Income Breakeven Point Q

QP = QV + F + C

Q = (F+C)/(P-V)
C: nominal cost of debt

Increasing debt will lower net income which will increase the net income breakeven point.

Sell also Operating Breakeven Point

Operating Breakeven Point

Operating Breakeven Point Q

QP = QV + F
Q = F/(P-V)

Sales Risk

Sales Risk (neither business risk nor operating risk) is the uncertainty with respect to the price and quantity of goods and services.

Financial Leverage

Definition 1:

Financial Leverage = (Total asset / Total equity)
(e.g.) DuPont analysis for ROE


Definition 2:

(Degree of) Financial Leverage = EBIT / (EBIT - Interest Expense)

EBIT = Operating income = Sales - Variable costs - Fixed costs

(Degree of) Operating Leverage

(Degree of) Operating Leverage = (S-V)/(S-V-F) = (P+F)/P

S:sales
V:variable costs
F:fixed costs

P=S-V-F: operating income

IFRS: Fixed Income Portfolio

Fixed Income Portfolio

Classification	Held-for-trading	Available-for-sale	Held-to-maturity
Unrecognized gains will be added to the investments' carrying cost(value)?	Yes	Yes

A Company's Fixed Income Portfolio (at yer end)

Bond	E	F	G	H
Classification	Held-for-trading	Available-for-sale	Held-to-maturity	Held-to-maturity
Cost (*)	$20,000	$35,000	$50,000	$60,000
Market value, end-of-year	$23,000	$45,000	$45,000	$64,000
Interest earned for the year	$1,000	$2,000	$4,000	$5,000

(*) All fixed income securities were purchased at par value.


At the year end, carrying value of the fixed income portfolio:
$20,000+$35,000+$50,000+$60,000 +($23,000-$20,000)+($45,000-$35,000)
=$23,000+$45,000+$50,000+$60,000
=$178,000

IFRS: Equity Portfolio

Equity Portfolio

Classification	Held-for-trading	Available-for-sale	Held-to-maturity	Associated Company (Equity method, no control)
Net Income	Dividend Unrealized P&L	Dividend	N/A	Share of Net Income
Designated at fair value? Unrecognized gain/loss would then be included in income?	No	Yes	No	No (*)

(*) If an equity-holding company is a manufacturing company and not a venture capital or mutual fund company, it may not account for its significant influence in the Associated Company using fair value.

A Company's Equity Portfolio (at yer end)

Stock	A	B	C	D
Classification	Held-for-trading	Available-for-sale	Available-for-sale	Associated Company
Cost	$100,000	$150,000	$250,000	$500,000
Market value, end-of-year	$97,000	$151,000	$257,000	$506,000
Dividends received during the year	$1,000	$2,000	$3,000	$4,000
The company's share of investee's net income for the year	$5,000	$7,000	$10,000	$15,000
Total Assets				$2,000,000
The company's ownership				40% (equity method)
The company has representation on the security's Board of Directors?				Yes
The company has effective control?				No
Proportionate consolidation instead of equity method				Net Income: Unchanged Total Assets: Increased ROA: Decreased (*)

The contribution of the equity portfolio to the company:
Net Income = ($97,000-$100,000) + $1,000 + $2,000 + $3,000 + $15,000 = $18,000


Net Income (If at acquisition, all of the equity securities that were eligible to be designed as investment at fair value were so designated, the amount that the entire equity portfolio would contribute to an equity portfolio-holding company's net income)
= ($97,000-$100,000) + $1,000 + ($151,000-$150,000) + $2,000 + ($257,000-$250,000) + $3,000 + $15,000
= $18,000 + $1,000 + $7,000
= $26,000


(*) Under the equity method, the cost, $500,000 will be included in total assets;
Under the proportionate consolidation method, the ownership(%) times Total Assets, 40% * $2,000,000 = $800,000 will be included in total assets.

Net Assets

Net Assets
= Net Non-Monetary Assets + Monetary Assets - Monetary Liabilities
= (Non-Monetary Assets - Non-Monetary Liabilities) + (Monetary Assets - Monetary Liabilities)

Pension Expense

Pension expense
= Service cost + Interest cost - Expected return on plan assets + Amortization of Unrecognized Prior Service Cost + Amortization of Unrecognized Loss

Pension Expense

	IFRS	U.S. GAAP
Net amount reported	may be different(*)	may be different(*)
Presentation	may be different(*)(***)	may be different(*)(**)
Use of expected return	OK	OK

(*) depending on the (1) treatment of prior service costs and (2) actual gains and losses
(**) net expense (income) is reported as a single amount
(***) various components of net pension expense (income) do not have to be presented as a single net amount

unstable minimum-variance efficient frontier

Mean-variance optimization models can generate unstable minimum-variance efficient frontiers.

Reasons for an unstable minimum-variance efficient frontier:

• absence of a short sales constraint
• historical beta

Accrual Tranche (CMO)

(e.g.) Investor's desired investment maturity and cash flow characteristics for CMO.

• investment maturity: long-term investment (average life greater than 5 years)
• cash flow characteristics: does not want to receive any cash flow from it for a number of years

Which type of CMO tranche would most likely meet this investor's desired investment maturity and cash flow characteristics?

A. An accrual tranche
B. A sequential-pay tranche.
C. A planned amortization class tranche.

A
Of the three, the accrual tranche typically receives principal only after all sequential-pay tranche and/or planned amortization class tranches have been paid off, meeting the investor's need for a long-term security.
Further, until its principal repayment begins, the accrual tranche does not pay interest but accrues it to principal, meeting the investor's need to not receive any cash flow for a number of years.

CFA Institute Research Objectivity Standards

• Firms must establish and implement salary, bonus, and other compensation for analysts that do not directly link compensation to investment banking or other corporate finance activities on which the analyst collaborated (either individually or in the aggregate.)
• Research analysts are prohibited from directly or indirectly promising a subject company or other issuer a favorable report or specific price target, or from threatening to change reports, recommendations, or price targets.
• Research analysts are prohibited from sharing with, or communicating with or communicating to a subject company, prior to publication, any section of a research report that might communicate the research analyst's proposed recommendation, rating, or price target. It is recommended that the compliance or legal department receive a draft research report before sections are shared with the subject company.
• Ensure that covered employees do not share information about the subject company or security with any person who could have the ability to trade in advance of or otherwise disadvantage the firm's all clients.

Soft Dollar Standards, I. General Principles

• Brokerage is the property of the client.
• (Incorrect) Mutual funds establish their own policies with respect to the use of certain brokers.

Standard III(A) Loyalty, Prudence And Care

• Voting proxies is an integral part of the management of investments.
• A fiduciary who fails to vote proxies may violate the Standard.
• A cost-benefit analysis may show that voting all proxies may not benefit the client, so voting proxies may not be necessary in all instances.
• Members and candidates should disclose to clients their proxy-voting policies.

Enterprise Value (AKA Firm Value)

Enterprise Value (AKA Firm Value) = Equity(Market Value) + Debt(Market Value)

Working Capital

Working Capital = Current assets(excluding Cash and Cash equivalents) - Current liabilities(excluding Notes payables)

Uncovered Interest Rate Parity

Uncovered interest rate parity is an economic theory about expectations.

i_FC - i_DC = E(S₁/S₀)

i_FC: expected interest rate of FC
i_DC: expected interest rate of DC
S₁, S₀: DC/FC
E(S₁/S₀): expected rate of change in the exchange rate

forward premium and discount

forward premium/discount = (forward rate - spot rate)/(spot rate)*(360/term in days)

or

forward premium/discount = (forward rate - spot rate)/(spot rate)*(12/# of months)*100%

forward rate, spot rate: FC/DC
forward premium/discount > 0: premium (DC appreciates against FC.)
forward premium/discount < 0: discount (DC depreciates against FC.)

Accounting Income (AKA Net Income)

Accounting Income
= (Operating Income Before Tax - Interest Paid) * (1 - Tax Rate)
= (Operating Income Before Tax - Capital Investment(#1) * Interest Rate) * (1 - Tax Rate)


(#1)(e.g.) Capital investment for an equipment. The equipment is to be financed entirely with a loan at an interest rate, with interest paid annually for the entire periods and full principal paid at the end of the year.

See also Net Income.

inflation effect adjustment (to forecasted cash flow)

inflation effect adjustment (to forecasted cash flow)

	Adjustment?	Inflation effect
Sales	Yes
Variable costs	Yes
Salvage value	Yes
Fixed cost	Yes	Reduces the value of tax savings including depreciation.
Depreciation	Yes	Ditto.

Balance Sheet Based Aggregate Accruals

Balance Sheet Aggregate Accruals: Change in Net Operating Assets
= ΔNet Operating Assets = ΔOperating Assets - ΔOperating Liabilities

ΔOperating Assets = ΔTotal Assets - ΔCash & Investments

ΔOperating Liabilities = ΔTotal Liabilities - ΔLong-term Debt(LTD) - ΔCurrent Portion of LTD

Stock Options and Stock Grants

Stock Options and Stock Grants

	Stock Options	Stock Grants
stock's volatility (given)	higher	higher
compensation expense	increased	not affected (*)
net income	decreased	not affected (*)

(*) Stock grants are based on the fair market value of the stock on the day of the grant.

Compensation Expense

Restricted stock grants(stock-based compensation):
(Annual) Compensation Expense = fair market value of the stock on the grant date / vesting period(*)

(*)(e.g.) The employee had to remain with the company for 3 years for the shares to vest; vesting period = 3 years in this case.

Net Operating Assets

Net Operating Assets = Operating Assets - Operating Liabilities

Operating Assets = Total Assets - Cash & Investments

Operating Liabilities = Total Liabilities - Long-term Debt(LTD) - Current Portion of LTD

Warranty Expense

Warranty Expense

period	previous	current
warranty expense	overestimated (*)
reserve	created	reversal (reduced)
expense	expensed	reduced
liability	created	reduced
net income	understated	increased

(*) actual claims < amounts accrued (and expensed)

Times Interest Earned (or Time Interest Earned)

Definitions of Times Interest Earned:

1. Times Interest Earned = EBIT/Interest expense
2. Times Interest Earned = Operating Income/Interest expense

Backwardation

• Backwardation refers to a situation where spot prices are higher than futures price—significant monetary benefits of the asset or a relatively high convenience yield can lead to this result.
• Positive roll yield.

commodity index

long-run geometric return of the average commodity ≈ 0
long-run geometric return of the commodity index > 0

-->Rebalancing of the index due to commodity price changes.

Because prices of individual commodities change, the index must be rebalanced, with:

• decreased allocation to commodities whose prices increased, and 
• increased allocation to commodities whose prices decreased.

Booth and Fama (1992) showed that the geometric return of a rebalanced portfolio is higher than the average return of its constituents.

commodities

commodities

roll yield	positive
contango/backwardation	backwardation futures price > "full carry" price As the contract approaches expiration, the futures contract will trade at a higher price compared to when the contract was further away from expiration. (convenience yield > risk free rate)
price level	(may be) historic low
price volatility	volatile
producers	Concerned that prices will fall further, to an unprofitable level. Will accept less that the "full carry" price in order to hedge price risk.

Capitalization

Capitalization = Long-term Debt(*) + Shareholder's Equity


(*) Or equivalently, Long-term Liablities

Capital

In a given context,

1. Capital = Total Assets or
2. Capital = Total Equity

Operating Income

Operating Income
= Revenue - COGS - SG&A expense - R&D expense
= EBIT + Depreciation(&Amortization)
= EBITDA

EBIT = Revenue - COGS - SG&A expense - R&D expense - Depreciation

Pretax Return on Capital

Pretax Return on Capital = EBIT/average of beginning and end of year capital(*)

(*) Total Assets

Convenience Yield

The benefit or premium associated with physically holding an underlying product or particular good, rather than the (futures) contract or derivative product for that good.


The futures price formula:
F₀=S₀*(1+r)^T+FV(CB,0,T)

where
FV(CB,0,T): the future value of the costs of storage minus the convenience yield

Thus convenience yield decreases the futures price.

futures contract value

The value of a futures contract before it has been marked to market can be greater or less than $0. The value is the gain or loss accumulated since the last marked to market.

currency forward

Counterparty risk
At expiration, if the market value of the contract is positive, the investor will only receive the agreed upon price if the other party does not default.

 

 

Price
Currency forward prices are determined by:

• current exchange rate
• current domestic interest rate
• current foreign interest rate
• maturity of the contract

CFA Institute Research Objectivity Standards: Standard 11

Firms should prohibit covered employees from communicating a rating or recommendation that is different from the current published rating or recommendation.

CFA Institute Research Objectivity Standards: Standard 2, potential conflicts of interest

Recommended disclosures relating to potential conflicts of interest in a subject company of the research:

• market making activities
• personal position / trading
• benefit received from the subject company

CFA Institute Research Objectivity Standards: Standard 5, Analyst compensation

• It recommends analyst's compensation be based on the accuracy of recommendations over time.
• Compensation should NOT be directly linked to investment banking or other finance activities.
• Compensation including an annual salary plus a bonus based on both (1) the accuracy of an analyst's recommendations over time and (2) the overall profitability of the company is appropriate.
• Making public disclosure of the extent to which research analyst compensation in general is dependent upon the firm's investment banking revenue is appropriate.

CFA Institute Research Objectivity Standards: Standard 6, Relationships with Subject Companies

Sharing any section of a research report

• Sharing any section of a research report that might commnicate the analyst's proposed recommendation, rating, or price target with the subject company is prohibited by the Standards.
• Sharing only the part of the analyst's report on the subject company that provides factual information (e.g. with the subject company's management) is allowed.

Allowing a corporate issuer to pay for an analyst's travel expenses:

• Violation of CFA Institute Research Objectivity Standards: Standard 6, Relationships with Subject Companies.
• Violation of CFA Institute Standard I(B), Independence And Objectivity.

regression analysis -- problems

regression analysis -- problems

	problem	Detect	Correct
Heteroskedasticity	Non-constant error variance (*2)	Breusche-Pagan	White-corrected standard errors
Autocorrelation	correlation among error terms	Durbin-Watson test (*1) for trend models Significance of the autocorrelations should be tested using the t-statistics for autoregressive models	Hansen method; adjusting standard errors
Multicollinearity	high correlation among Xs	if F-test significant, t-tests insignificant	dropping X variables

(*1) positive autocorrelation if DW < d₁

(*2) Conditional Heteroskedasticity
Variance of the error term is correlated with the values of the independent variables.

VaR (value-at-risk)

• VaR is an ineffective statistical measure of risk when a hedge fund has higher turnover or frequent changes in its strategy.
• If VaR solely utilizes historical data as inputs, it does not provide a reliable estimate of future risk.

hedge fund index

Problems:

• hedge fund listing issues (hedge fund selection)
• exclusion of certain hedge funds
• data verification issues
• turnover
• survivorship bias
• backfill bias
• estimation bias
• due to the closing of funds to new investors
• autocorrelation
• short performance history of hedge funds

Maximum Drawdown

• The largest loss from peak to trough a hedge fund has experienced over a certain period of time.
• The larger the maximum drawdown, the greater the market disruption risk associated with the particular hedge fund.
• The risk of long-tail events resulting from major market disruptions should be a key concern of investors. A measure of such long-tail event is maximum drawdown.

Equity Swaption

Equity Swaption

long	(Fixed-rate) Payer swaption	(Fixed-rate) Receiver swaption
pay	Fixed-rate	Equity index return
receive	Equity index return	Fixed-rate

cheapest tranche

A tranche with a maximum OAS/Option cost is the cheapest.

PAC collar

If the prepayment speed falls within the PAC collar, then the tranche receive the principal payments as scheduled.

Overcollateralization (of the home equity loan ABS)

(e.g.)
Total principal of tranches = $450 * 10⁶
Total principal of collateral = $475 * 10⁶

Overcollateralization = ($475-$450)*10⁶ = $25*10⁶

Default of collateral = $30 * 10⁶

Overcollateralization - Default of collateral
= $25*10⁶ - $30 * 10⁶
= -$5*10⁶

Principal of subordinated tranche (prior to the default)
= $54*10⁶

Principal of subordinated tranche (after the default)
= $54*10⁶-$5*10⁶
= $49*10⁶

Credit Enhancement

Credit Enhancement

	internal/external	Credit Card Receivable ABS
Excess servicing spread	internal	The ABS issuer pays a coupon to investors that is less than the coupon earned on the collateral. The excess of cash inflows over cash outflows is used to fund credit losses in the collateral.
Letter of credit	external	A letter of credit is a third party, usually a bank, guarantee against collateral losses up to a certain point. Defaults on the collateral are thus mitigated to a certain extent. The third-party guarantees are subject to the weak-link philosophy and any credit downgrades associated with the third party will negatively affect the rating of the ABS.
Overcollateralization	internal	Total principal of collateral > Total principal of tranches (Total principal of collateral - Total principal of tranches) = extra collateral When (Total principal of collateral - Total principal of tranches) < 0, collateral defaut would first be absorbed by the extra collateral. Then losses from defaults (a credit event) are absorbed by subordinated tranche until the principal backing the tranche is exhausted. Home equity loan ABS.

Auto Loan ABS and Credit Card Receivable ABS

Auto Loan ABS and Credit Card Receivable ABS

	Auto Loan ABS	Credit Card Receivable ABS
Collateral	The collateral structure for ABS backed by amortizing assets (e.g. auto loans) generally does NOT change once the security is issued. The collateral simply gets smaller as the loans are paid off by the borrower.	The collateral structure for ABS backed by nonamortizing assets (e.g. credit card receivables) does change during the lockout period. During the lockout period, principal payments on the collateral are used to purchase additional collateral assets. (revolving structure) A call provision, which causes cash flows to be directed at principal reduction rather than purchasing new collateral assets, is usually included. (e.g.) Cleanup call, which is triggered by a decline in the value of the collateral.
Credit Enhancement
Prepayment Risk	Interest rate movements (up or down) are unlikely to have a significant effect on the prepayment rate of the auto loan ABS. Borrowers who take out an auto loan generally do not refinance their vehicles as interest rate decline. Because auto loans are short-term loans and the underlying asset (the automobile) has a tendency to rapidly depreciate in the early years, there is little incentive for borrowers to repay the loan even if interest rates decline.	During the lockout period, any principal (pre)payments are used to purchase additional collateral for the ABS. Thus, any changes in prepayment rates induced by interest rate changes would be offset by additional purchases of collateral. A contraction, or extention would be unlikely to occur.

Normalized EPS

P/E ratio based on the normalized EPS = Current stock price / Normalized EPS 

• using the method of average EPS
Normalized EPS (based on average EPS) = average EPS over the sample period

• using the method of average ROE

Normalized EPS (based on average ROE) = average ROE over the sample period P/E ratio based on the normalized EPS = Current stock price / (average ROE over the sample period * BVPS (latest))

---

(Question)

Year		2008	2007	2006	2005
BVPS		$25.58	$33.62	$37.54	$32.26
ROE		3.2%	4.0%	4.5%	3.9%

Based on the method of average return on equity (ROE), the normalized EPS is closest to:

Answer:

Year		2008	2007	2006	2005
BVPS		$25.58	$33.62	$37.54	$32.26
ROE	Average ROE = 3.9% (*1)	3.2%	4.0%	4.5%	3.9%
Normalized EPS	$1.00 (*2)

(*1) (3.2%+4.0%+4.5%+3.9%)/4 = 3.9%
(*2) 3.9% * $22.58 = 0.9976... = $1.00

emerging market valuations

emerging market valuations

should be adjusted for country risk?	Yes
- adjusting cash flows?	Yes(*)
- adjusting discount rate?	No(*)
companies within an emerging market will be affected differently by country risk? (e.g. exporters and importers)	Yes
country risk for foreign investors > that for local investors	Maybe
Is country risk asymmetric / one-sided?	Yes (*)

(*) Because many emerging market companies have risk profiles that are one-sided (down only). It is best to adjust for this in the cash flows rather than adjust the discount rate.

• When estimating the percent of debt and equity in the capital structure, the debt and equity weights from a global industry index should be used, not the market value of the firm's debt and equity, nor the book value.
• Firms in emerging markets often use debt conservatively and this results in lower leverage ratios than for firms in the same industry in other countries.
• The industry beta, not the individual firm beta, will be needed to obtain the cost of equity capital in the CAPM. The beta should be estimated for the company's industry by regressing the company's industry returns against a well diversified global index, not the local market index.

flow-through of inflation (inflation flow-through)

inflation flow-through (flow-through of inflation)

in the absense of full-flow-through of inflation:
inflation of a country where the company operates	low	high
P/E ratio	higher	lower

P/E reflecting the effect of inflation
= 1 / (R_r+((1-IFTR)*i))

R_r: real required rate of return
IFTR: inflation flow-through rate
i: inflation rate

Residual Dividend Policy

A firm

1. determines the optimal capital budget
2. uses retained earnings to fund the optimal capital budget
3. pays out what is left over to shareholders

This policy results in:

• unstable dollar dividend paid to shareholders
• making the firm able to use internally generated funds to a greater extent when deciding how to fund the optimal capital budget
• higher return on equity (cost of equity capital) due to uncertainty related to dividend payments

Bird-in-the-hand Theory

Bird-in-the-hand Theory

	investors' response	cost of equity	equity value
assurance of receiving a higher dividend today	positive	lower	higher
waiting for returns in the form of capital appreciation	negative
stock repurchase	(*) does not provide the same assurance as dividends
unstable dividends	(apart from the theory, generally) negative

(*) It is an unpredictable and possibly one-time event.

target payout ratio approach

increase in dividends = increase in earnings * target payout ratio * adjustment factor

adjustment factor = (1/t)

t:moving toward the target payout ratio over the time peiod t

unamortized past service cost

unamortized past service cost

	IFRS	U.S.GAAP
unamortized past service cost	eliminated from funded status (PBO)
pension liability (PBO)	lower
funded status	higher

Fair Market Value of Plan Assets

Fair Market Value of Plan Assets (t, end) =
Fair Market Value of Plan Assets (t-1,end; t,beginning)
+ Actual retun on plan assets (t)
- Benefits paid (t)
+ Contribution to the pension plan (t)

Fair Market Value of Plan Assets (t, end): AKA beginning balance plan assets
Fair Market Value of Plan Assets (t-1,end; t,beginning): AKA ending balance plan assets

Guideline Transaction Method (GTM): Discount for Lack Of Control (DLOC) and Discount for Lack Of Marketability (DLOM)

One prepared a database of price multiples from the sale of entire public and private companies to obtain the appropriate price multiples for a small and private company:

• When valuing a noncontrolling equity interest
• DLOC: Discount for Lack Of Control
• (1 - DLOC)(1 + Control Premium) = 1
• DLOC = 1 - (1/(1 + Control Premium))

• When valuing a company considering that its (equity) interest cannot be easily sold
• DLOM : Discount for Lack Of Marketability
• 1 - Total Discount = (1 - DLOC)*(1 - DLOM)
• Total Discount = 1 - ((1 - DLOC)*(1 - DLOM))

income approach valuation: Capitalized cash flow method, Free cash flow method, and Excess earnigs method

income approach valuation: free cash flow method, excess earnigs method, capitalized cash flow method

method	free cash flow	excess earnings	capitalized cash flow
stage	single or plural (e.g., two)		single
constant growth assumption?			Yes
intangile assets to value?		Yes

Operating Income After-Tax

Gross Profit = Revenue - COGS

Pro forma EBITDA = Gross Profit - SG&A expenses

Pro forma EBIT = Pro forma EBITDA - Depreciation expenses

Operating Income After-Tax = Pro forma EBIT - Pro forma taxes on EBIT

Investment Value

• The value to a specific buyer.
• May be different for each investor due to variant:
• cash flow estimates
• perceived firm risk
• discount rates
• financing costs
• synergies (that lead to decreased costs)

private firms and public firms

private firms and public firms

firms	private	public
market cap	smaller	larger
risk	higher	lower
risk premium	higher	lower
required returns	higher	lower
access to liquid public equity markets?	No	Yes
as many qualified applicants for top positions as public firms?	No	Yes
depth of management	reduced
growth	slow
investors' time horizon	long-term	short-term
managers' time horizon	long-term	short-term
substantial equity ownership by management?	Yes	No

covered interest rate parity

1 + r_DC = (1 + r_FC) * (forward rate)/(spot rate)

If
1 + r_DC > (1 + r_FC) * (forward rate)/(spot rate)
then borrow in FC and invest in DC.


forward rate, spot rate: DC/FC

unexpected restrictive fiscal policies

unexpected restrictive fiscal policies

budget deficit	unexpectedly reduced
economy	(could result in) a slowdown
inflation	(could be) lower
imports	discouraged
exports	encouraged
home country currency value	higher
government borrowing	decline
real interest rate	down
investment funds to the home country	flow out of the country
home country currency value	lower
short-run effect (*)	devaluation of the home country's currency
aggregate demand	decrease
domestic interest rate	decrease (**)
imports	reduce
Current account deficit	reduce
foreign investment	lower
domestic capital	leaving the country
Capital account surplus	reduce

(*) Since financial capital is mobile, the effect of the interest rate change generally dominates in the short run, leading to short-run devaluation.

(**) due to less government borrowing

unexpected restriction of the monetary supply growth

unexpected restriction of the monetary supply growth

monetary supply growth	unexpectedly restricted
interest rates	up
foreign interest rates	(regarded as) constant in this case
home country's interest rate differential	increase
home country's currency value	increase
quantity of the home country's currency traded	unchanged (*)
volatility of home country's currency values	quite high

(*) This is because the supply of the home country currency is decreasing (the supply curve shifts up and to the left) and the demand for the home country currency is increasing (the demand curve shifts up and to the right), resulting in a higher exchange rate with quantity unchanged.

foreign currency bid-ask spread

Bank and other currency dealer positions are NOT considered to directly impact the size of foreign currency spreads. If a dealer wants to reduce his or her holdings, he or she will usually adjust the mid-point of the spread rather than the spread itself.

• To uload an excess inventory of the foreign currency:
• Reduce his or her foreign currency ask (selling price)
• Reduce his or her foreign currency bid (buying price) (*)
• The spread would remain relatively unchanged.

(*) So that he or she does not buy any additional foreign currency.

conversion value of a convertible bond

conversion value of a convertible bond = price of common stock * conversion ratio

hard put

A bond with an embedded hard put is redeemable through the issuance of

• cash

soft put

A bond with an embedded soft put is redeemable through the issuance of

• cash
• subordinated notes
• common stock
• any combination of these three securities

yield volatility

• follows patterns over time that can be
• modeled
• and used to forecast volatility using autoregressive statistical models

implied volatility

Using:

• observed prices for derivatives
• option pricing models

Assumptions:

• The option pricing model is correct.
• The implied volatility is constant.

revenue-backed securities

Important factors in an analysis

• ability of the municiparity to change the rate or user-charge
• This will be governed by the rate covenant in the bond which will determine the level of revenue generated by the project.
• priority of revenue claims
• whether or not other government entities can access revenues from the underlying project before bondholders

adjusted book value

adjusted book value
= Total liabilities & equity(*) + PV of operating lease + Capitalized R&D expense (net of depreciation) - (Current liabilities + Total debt + PV of operating lease)


(*) i.e., Total assets

residual return on capital (RROC)

RROC = EVA/Capital(*)

(*) or total adjusted capital base

EVA = Net Operating Profit After Taxes (NOPAT) - (Capital * Cost of Capital)
= NOPAT - $WACC
= EBIT(1-tax rate) - $WACC

adjusted NOPAT (net operating profits after taxes)

adjusted NOPAT = Revenue - COGS - SG&A - R&D (Expense) Amortization - Depereciation expense + Implied interest expense on operating lease - Cash operating taxes(*)

(*) This amount includes all appropriate tax adjustments.

sustainable growth

1. Sustainable growth is growth that can be achieved by:
• retaining some earnings
• keeping the capital structure (debt to equity) constant
2. The sustainable growth rate is the rate of dividend and earnings growth that can be sustained for a given return on equity assuming that:
• additional debt capital may be raised
• keeping the capital structure constant

---

(Question)

How should sustainable growth be described?
The sustainable growth rate is the rate of dividend and earnings growth that can be sustained for a given return on equity, assuming that:

A. no additional external capital is raised.
B. additional debt capital may be raised, keeping the capital structure constant.
C. additional equity capital may be raised proportional to the amount of earnings retained.

Answer: B

hyperinflationary environment

hyperinflationary environment

• IAS accounting standards allow the parent to translate an inflation-adjusted value of the nonmonetary assets and liabilities of the foreign subsidiary at the current inflation rate, removing most of the effects of high inflation on the value of the nonmonetary assets and liabilities in the reporting currency.
• In a hyperinflationary environment, the parent company can reduce translation losses by reducing its net monetary assets or increasing its net monetary liabilities.
• In order to do this, the parent should issue debt denominated in the subsidiary's local currency and invest the proceeds in fixed assets for the subsidiary to use in its operations.

Bear Hug

1. In a situation of the hostile merger, the acquiring company may initiate a bear hug in which the merger proposal is delivered directly to the board of directors of the target company in the hopes of gaining board support for the proposed merger before management can react to the proposal.
2. If the bear hug is not successful, the acquirer may appeal directly to the target's shareholders:
• through a tender offer in which the acquirer offers to buy shares directly from shareholders or
• through a proxy fight in which a proxy solicitation is used to convince shareholders to elect a board of directors chosen by the acquirer. The board of directors would then replace the target company's management and allow the merger to move forward.

Synergistic Value and Acquirer's Gain

Synergistic value
V_AT = V_A + V_T + S - C

Also V_AT - V_A = S - C + V_T

where:
V_AT = the combined value of the firm
V_A = the value of the acquirer before the merger
V_T = the value of the target before the merger
S = the synergistic value from the merger
C = the cash paid to the target


Acquirer's gain
Acquirer's gain = S - (P_T - V_T)
= S - C + V_T
= V_AT - V_A

where:
S = the synergistic value from the merger
P_T = the price paid for the target; P_T = C, if only cash is paid to acquire the company.
V_T = the value of the target before the merger

tax losses accumulated

If the target of a merger has unused tax losses accumulated, the merged company can use the tax losses to immediately lower its tax liability, thus increasing its net income.

(domestic) CAPM and international CAPM (ICAPM)

Similarities

• investors are risk averse
• all investors have uniform expectations of risk and return on all assets
• all investors hold some combination of a risk-free asset and the market portfolio

Differences

• market portfolio
• domestic CAPM: all domestic assets
• international CAPM: constructed out of the global universe of risky assets
• currency hedging
• domestic CAPM: N/A
• international CAPM: ICAPM breaks down if currency hedging is not available as a result of physical or legal restrictions  on such activities.

bond investment in foreign country

bond investment in foreign country

foreign nation's economic activitiy	improve
real interest rate (of foreign currency)	increase
bond price (in foreign currency)	down
foreign currency (vs. domestic currency)	appreciate (*)

(*) It offsets the loss on the bond in domestic currency.

correlation between stock prices and the local currency

correlation between stock prices and the local currency

correlation between stock prices and the local currency	positive
foreign stock price	decrease
local currency	depreciate

functional form model misspecification

• By pooling across the two very different sample periods, the regression becomes an example of a misspecified functional form.

R-Squared

R²
= (regression sum of squares)/(total sum of squares)
= (regression sum of squares)/(regression sum of squares + error sum of squares)

---

If R² > 50%, then
R²
= (regression sum of squares)/(regression sum of squares + error sum of squares) > 50%

∴ (regression sum of squares) > (error sum of squares)

---

A low R² in the regression (equation) indicates that the slopes in the equation are very close to zero, indicating that the dependent variable is unaffected by the independent variables. For instance, if all the slopes in the equation equals zero, then the dependent variable equals the intercept(a₀, which is constant over time).

P-value

P-value = Probablity of making Type I error

The p-value is the probability that the null hypothesis H₀ is true (and incorrectly rejecting it).

The decision rule is to reject the null hypothesis if the p-value < significance level (i.e., there is only a very small chance that the null hypothesis is correct(=true)).

futures and forward

futures and forward

	futures	forward
interest rate environment	flat (constant)	flat (constant)
price	same	same
marked to market?	Yes (each day)	No
credit risk	lower	higher (*)

(*) Without mark to market, large losses are allowed to accumulate.

Cash Flow Duration

• One prepayment rate will apply over the life of an MBS for whatever change in interest rate is assumed.

Cash Flow Yield (CFY)

• One method of valuing mortgage backed securities.
• Dependent on prepayment assumptions; if prepayment rates differ from the assumption, the CFY will not be realized.
• Reinvestment assumption (weakness): Interim cash flows are reinvested at the CFY.

home equity loan-backed securities

home equity loan-backed securities

-backed securities	home equity loan	auto loans	credit card receivables
interest rate change	declining	declining	declining
relative nominal spread	high
risk of prepayment	increase	(*)	(*)

(*) increase less than home equity loan backed securities

country risk

• Country risk can be largely diversified away.
• Hence, the addition of country risk to discount rates is not the preferred way for valuing emerging market stocks.
• Scenario discounted cash flow method is recommended as the prime valuation approach.
• A common method for deriving a country risk premium does use the spread between U.S. Treasuries and local bonds that are dollar denominated, but this approach is realistic ONLY if the returns of local debt and equity investments are highly correlated.
• Such a premium is difficult to apply to individual securities because different industries are affected by country risks in different ways.

closed-end country fund

• immediate diversification within the subject country
• more volatile than their underlying assets due to the added volatility induced by the fund premium to net asset value
• strongly correlated with the U.S. stock market
• inferior substitute for direct investing even for most emerging markets

The closed-end country fund premiums to net asset value:

• very volatile
• add to the risk (but NOT return) of the fund
• decrease as the country liberalizes foreign acces to their financial markets

three-stage dividend growth model

The terminal value in the three-stage dividend growth model can be estimated using the:

• Gordon growth model or
• price-multiple approach

stages of growth

stages of growth

phase	initial growth	transition	maturity
earnings	rapidly increasing
dividends	little or no
reinvestment	heavy
ROE & required return on the stock (r)	ROE > r
FCFE	negative (*)
profit margin	high

(*) due to heavy capital investment

carve-out transaction

• A new entity is created in a similar manner to the spin-off transaction.
• The main difference is that minority of shares is sold to the public while the majority portion of the new shares are held by the parent company (they are not distributed to existing shareholders).

spin-off transaction

• Creating a new entity out of a company's business line or one of its subsidiaries
• and then granting shares in the new entity to the existing shareholders of the parent company.
• The shareholders are then free to sell their shares in the spin-off company in the marketplace.
• Generally seen as a favorable sign in the market due to expected greater efficiency for the spin-off company and the parent company.

See also carve-out transaction.

bankruptcy

The chances of bankruptcy are much greater with a heavy reliance on debt financing (higher D/E ratio). It increases the cost of debt (or equity).

net agency costs of equity

Agency costs

• Equity holders' cost to monitor the firm's executives, management's bonding costs to assure owners that their best interests are guiding the company's actions, and residual losses that result even when sufficient monitoring and bonding exists.

Adding additional debt reduces the agency costs to equity holders since less of their capital is at risk. The leverage effectively shifts some of the agency costs to bondholders. Additionally, managers have less cash to squander when higher leverage is employed since higher interest costs will restrict discretionary free cash flow.

Weighted Average Cost Of Capital (WACC)

WACC = (E * R_e)/(E+D) + (D * R_d * (1-t))/(E+D)

E: market value of the firm's equity
R_e: cost of equity
D: market value of the firm's debt
R_d: cost of debt
t: corporate tax rate

• If you have several capital structure plans, the plan with lowest WACC maximizes the firm's stock price and thus reflects the optimal capital structure.

bootstrap earnings effect

preconditions:

• If an acquirer issues common stock at the current market price and uses the proceeds to acquire the acquiree's outstanding common stock.
• Acquirer's P/E (pre-merger) > Acquiree's P/E (pre-merger)
• 
  Acquirer's P/E (pre-merger) ≤ Acquirer's P/E (post-merger)
• Acquiree's acquisition price is the current price or lower.

Then the bootstrap earnings effect on post merger earnings (*) would most likely occur.

(*)Acquirer's EPS (post-merger) > Acquirer's EPS (pre-merger)

synergies

If the companies have different product lines, synergies in the form of

• cost savings or
• revenue enhancement

are unlikely to occur.


If the companies are in very different industries, a merger is unlikely to make increased market power in either industry.

money demand model and traditional model

traditional model and money demand model

	traditional model	money demand model
real economic activity	N/A	increase
Stock in DC	up	up
DC	down (depreciation)	up (appreciation)(*)

DC: Domestic Currency

(*) due to an increase in the demand for the domestic currency

extended CAPM

Preconditions:

• Global investors have identical consumption baskets.
• Purchasing power parity (NOT interest rate parity) holds throughout the world.
• Exchange rates are predictable (no real exchange rate risk)

Do not confuse the extended CAPM with the international CAPM. The international CAPM does not require the two additional assumptions that the extended CAPM does.

Conditional Heteroskedasticity

A regression exhibits conditional heteroskedasticity if the variance of the regression errors:

• are not constant
and
• changes as function of the regression independent variables.

The squared residual (i.e, residual is the estimated error) is used to proxy the error variance.

serial correlation

• correlation between the regression errors across time ~ 1
• the presence of significant positive serial correlation

• positive serial correlation
• standard errors to be too small
• too large t-statistics (biased upward)

Net Present Value (NPV), Internal Rate of Return (IRR), and Direct Capitalization Method

• Net Present Value (NPV)
• If a cash flow fluctuates, the best valuation approach is the net present value.
• Internal Rate of Return (IRR)
• Limitation: multiple solutions when the investment has positive cash flow one year and a negative cash flow the next year.
• Direct Capitalization Method
• Best used when the investment's net operating income is stable.

NPV > 0
then IRR > required rate of return

After-Tax Cash Flow

(e.g.)

After-Tax Cash Flow

Year	Operating income	Tax Payable
1	$400,000	$40,000
2	$420,000	$42,000
3	$441,000	$44,000
4	$463,000	$46,000
5	$486,000	$49,000
After-tax equity reversion	$2,000,000

loan-to-value ratio = 75%
equity contribution = $1,000,000
cost for loan = 8%
loan amortization period (annual payments) = 20 (years)

---

Based upon the information presented in the exhibit above, the after-tax cash flow for year 2 is:

total value = $1,000,000 / (1-75%) = $4,000,000

debt = total value - equity contribution = $4,000,000 - $1,000,000 = $3,000,000

-3,000,000 PV
8 I/Y
20 N
0 FV
CPT PMT 305,556

After-Tax Cash Flow

	Year 2
Net Operating income	$420,000
Less:Annual debt service	($305,556)
Before-tax cash flow	$114,444
Less:Tax payable	($42,000)
After-tax cash flow	$72,444

band-of-investment method

(e.g.)

band-of-investment method

Property Type	Net Operating income	Growth rate	Property value	Loan-to-value
Hotel	$900,000	7%	$9,000,000	70%

return of capital to the lender = 0.02185

Hotel cap rate = market rate of capitalization = $900,000 / $9,000,000 = 10%
Return on funds = Cost of loan = i = 8% (given)
Loan = 20 years

Return of capital to lender = i/((1+i)ⁿ-1) = 0.08/((1+0.08)²⁰-1) = 0.02185
Mortgage constant = Return on funds + Return of capital to lender = 0.08 + 0.02185 = 0.10185

		Rate	Weighted
Loan	70%	0.10185	70%*0.10185 = 0.0713
Equity	30%	0.0957 (*2)	0.10-0.0713 = 0.0287
Total	100%		10% (*1)

(*1) Hotel cap rate

(*2) Equity dividend rate (required cash-on-cash return) = 0.0287 / 30% = 0.0957

Cross-sectional regression

Cross-sectional regressions have unknown predictive power outside the

• specific sample and
• time period

used to generate the regression.

Multicollinearity

• The inclusion of independent variables which are correlated with the existing independent variables causes the multicollinearity:
• standard errors: biased upward
• t-statistics: biased downward (deflated)
• If multicolinearity is present in a model, the interpretation of the individual regression coefficients become problematic.
• The existence of multicolinearity is generally signaled by
• High R2 value (e.g. 81%)
• Low t-statistics on the regression coefficients (<2; approximate critical value = 2)

Justified price-to-sales (P/S) ratio

Justified price-to-sales (P/S) ratio
= P₀/S₀ = (D₁/(r-g))/S₀
= (E₁d/(r-g))/S₀ = (E₀(1+g)d/(r-g))/S₀
= (E₀/S₀)*d*(1+g)/(r-g)
= (Net) profit margin * Payout ratio * (1+g)/(r-g)

Justified price-to-book value (P/B) ratio

Justified price-to-book value (P/B) ratio = P₀/B₀ = (ROE-g)/(r-g)


P₀ = D₁/(r-g)
g = ROE * (1-d) = ROE - ROE * d
ROE * d = ROE - g

Justified price-to-book value (P/B) ratio
= P₀/B₀
= (D₁/B₀)/(r-g)
= (E₁/B₀)*d/(r-g)
= ROE*d/(r-g)
= (ROE-g)/(r-g)

vertical merger

Vertical merger (into new and different industries) would be more likely to increase risks and the cost of capital.

financial analysis framework

1. First phase
• Input: The institutional guidelines related to developing the specific work product (defining the purpose and context of the analysis)
2. Data collection phase
• Input: Audited financial statements
3. Data processing phase
• Output: Ratio analysis

long-term debt-to-equity ratio, calculated immediately after the acquisition

Under U.S. GAAP,

long-term debt-to-equity ratio = (BV of acquirer's long-term debt + FV of acquiree's long-term debt)/(BV of acquirer's shareholders' equiy + FV of shares used to acquire + non-controlling interest)


FV of shares used to acquire + non-controlling interest
= FV of shares used to acquire / %Purchased(*)

(*) %controlling interest in the purchased company

Partial goodwill method

Fair value of the purchased company = Purchase price / %Ownership interest

Goodwill
=Purchase price - Identifiable net asset(@fair value) * %Ownership interest

Full goodwill method

Fair value of the purchased company = Purchase price / %Ownership interest

Goodwill
=Fair value of the purchased company - Identifiable net asset(@fair value)

Amortized Discount (a.k.a. Discount Amortization)

• Held-to-maturity securities are reported on the balance sheet at amortized cost.
• Carrying value = Issue Price + Amortized Discount
• Amortized Discount = Issue Price * Interest Rate - Face Value * Coupon Rate

Deregulation

Deregulation

Effect	short-run	long-run
High-cost producers	exit the industry due to lower profits	N/A
Quality of goods and services	may decline
Prices	may rise	should fall
Unions	become less powerful
Employers	may be laid off
Industries		more competitive as barriers to entry fall

Capture Hypothesis

• When the regulatory decisions favor an industry, this can be due to the fact that the regulatory bodies tend to have members who used to work in the industry.
• Regulatory decisions will favor industry because the industry has greater economic resources and incentives than consumers.

Share-the-gains, share-the-pains theory

• The pains and gains of regulation would be shared equally between the industry (producer) and consumer.

The share-the-gains, share-the-pains theory holds that regulators' main objective is simply to keep their jobs and to take into account the needs of legislators, consumers, and industry.

Feedback Effect

A feedback effect is an example of a creative response, where the intent of the original regulation is undermined.

(e.g.)
When airbags were required in automobiles, consumers started wearing seat belts less often and driving at higher speeds because the airbags gave them a feeling of greater safety. Consequently, driving fatalities and injuries did not decline as much as expected.

Creative Response

In a creative response, the regulated parties conform to the letter but not the intent of the law.

social regulation

Social regulation (which includes an environmental regulation):

• Increase production costs that will burden smaller businesses more than larger businesses
• Less competition within an industry.
• The higher production cost from the social regulation will ultimately be absorbed by consumers.

currency swap, interest rate swap and equity swap: credit risk

currency swap, interest rate swap and equity swap: credit risk

swap's life	Beginning	Middle	End
currency swap	Low(*1)	Increase(*2)	High(*4)
interest rate swap	Low(*1)	Increase(*2)	Decline(*3)
equity swap		Highest (*5)

(*1) Because each counterparty accepted the creditworthiness of the other in order to initiate the swap transaction. Additionally, net value of the swap for each party is set as zero.

(*2) By the middle of the swap's life, payments are coming due and credit risk increases.

(*3) As the remaining payments were made towards the end of the swap's life.
 
(*4) With the exchange of notional principal, the final payment keeps credit risk high through the end of the swap life, causing it to peak between the middle and the end of the swap's life.

(*5) At the end of the swap there are few potential payments left and the probability of either party defaulting on their commitment is relatively low.

Swap Spread

Swap Spread = Fixed rate - Reference rate

• The swap spread is derived from the term structure of interest rates used to price the cash flows of the swap. These rates do not reflect the credit risk of the counterparties. They reflect the credit risk in the overall global economy (general level of credit risk in the marketplace) because they reflect the credit spread of the reference rate used to calculate the fixed-rate and expected floating-rate payments.
• The fixed rate on any particular swap is the same for any interested party regardless of their credit quality.

CMBS (Commercial Mortgage-Backed Securities)

• CMBS are collateralized using non-recourse loans on commercial (i.e., income-producing) properties.
• Non-recourse means that the only cash flow support provided from the loan comes from the ability of the property to generate income and from the value of the property itself.
• The lender cannot seize personal assets of the borrower to satisfy any portion of the unpaid obligation.

MBS

(e.g.)

MBS

MBS	Effective duration	OAS	Z-spread	Option cost(*2)	OAS/Option cost
W	(*1)	0.28%	0.79%	0.51%	0.5490
X	(*1)	0.49%	1.16%	0.67%	0.7313 (*3)
Y	(*1)	0.31%	1.12%	0.81%	0.3827
Z	(*1)	0.40%	1.14%	0.74%	0.5405

(*1) approximately the same
(*2) Option cost = Z-spread - OAS
(*3) This MBS will add the most value relative tot the risk associated with the security because the MBS-X has the highest OAS realtive to the cost of the option embedded in the MBS. Therefore, it is the most attractive of the four alternative.

unlevered beta

β_u = 1/(1+D/E)*β_E
= E/(D+E)*β_E

β_u * (D+E) = E * β_E


β_u: unlevered beta
β_E: levered beta (beta of the company with debt D and equity E)

Private equity

Percentage management fee = management fee / paid-in capital
paid-in capital = Σcalled-down (capital)


When
NAV before distribution₁ > Committed capital,

Carried interest₁ = (NAV before distribution₁ - Committed capital) * %Carried interest

Carried interest₂ = (NAV before distribution₂ - NAV before distribution₁) * %Carried interest


NAV after distribution = NAV before distribution - Carried interest - Distributions


Post-money valuation = V/(1+r)^t

---

Adjusted post-money valuation discount rate = r'
π: probability of risk of failure


(1+r')(1-π)=1+r
(1+r')-π(1+r')=r'(1-π)+1-π=1+r
r'(1-π)=r+π


r'=(r+π)/(1-π)
= (1+r)/(1-π) + (-1+π)/(1-π)= (1+r)/(1-π) - 1

Capital budgeting process (Level 2)

• The capital budgeting process should not consider sunk costs (i.e., past costs that do not affect the cash flows of the project)
• (e.g.) costs to find investment projects
• The capital budgeting process should consider the economic impact from increased competition resulting from highly profitable investment projects.

Divestiture

Divestiture should be a rate event. A divestiture usually sends a negative signal. I it unlikely that investors want management to sell profitable assets.

Joint Venture

joint venture

Method	Equity	Proportionate consolidation
Total assets	Low	High (*2)
Total liabilities	Low (*4)	High (*2)
Total equity	same	same
Revenue	N/A (*1)	High (*5)
Expense	N/A (*1)	High (*5)
Net income	same (*3)	same (*3)

(*1) None of the joint venture's revenues and expenses are reported under the equity method.
(*2) Including pro-rata ownership of the separate assets and liabilities of the joint venture. The investment in the joint venture is NOT included as an asset.
(*3) The proportion of income from the joint venture is reported separately, so that net income is the same under either method.
(*4) None of the joint venture's debt is reported by the investing company.

(*5) The proportionate share of the purchased firm's revenue and expenses would be reported on the joint venture holding company's income statement, increasing both revenues and expenses.

Purchasing Power Parity

Absolute purchasing power parity

• Absolute purchasing power parity is based on the law of one price, which states that a good should have the same price throughout the world. Absolute purchasing power parity is not widely used in practice to forecast interest rates.

Relative purchasing power parity

• Although relative purchasing power parity is useful as an input for long-run exchange rate forecasts, it is not useful for predicting short-run currency values.

Domestic Fisher Relation

1 + nominal interest rate = (1 + real interest rate) * (1 + expected inflation rate)

currency: interest rate, inflation, and appreciation/depreciation

• Economic growth
• An increase in U.S. economic growth would weaken the dollar because the economic growth would stimulate the demand for imports and foreign currencies. This would result in a weakening of the dollar, relative to other currencies.
• Unexpected expansionary fiscal policy
• increase in real interest rate and then appreciation of the currency
• higher inflation, economic growth, and more imports --> depreciation of the currency
• However, financial capital is more mobile than the goods market so the overall short-run effect would be for the currency to appreciate

ANOVA (Analysis of Variance) Table

ANOVA (Analysis of Variance) Table provides data on the source of variation in the dependent variable (e.g. stock returns).

• Degree of freedom for the regression sum of squares (a.k.a., the "explained sum of squares") = k (the number of independent variables)
• Degree of freedom for the error sum of squares = N - k - 1
• Degree of freedom for the total sum of squares(*) = N - 1

(*)The total sum of squares equals the numerator of the sample variance formula for the dependent variable. The denominator in the sample variance (N-1) equals the degrees of freedom for the numerator (the total sum of squares).

F-statistic test (F-test)

• A test for the overall significance of the regression, which is formulated with the null hypothesis that all slopes (independent variables' coefficients) simultaneously equal zero.
• This null hypothesis is identical to a test that the R-square = 0.

F = (explained variance) / (unexplained variance)
= mean regression sum of squares / mean squared error
= (regression sum of squares/number of independent variables) / (error sum of squares/degrees of freedom;error)

= (RSS/k) / (ESS/(n-k-1))