Hedge Fund Index

Problems

• hedge fund listing issues
• 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
• selection bias
• Strict rules for inclusion and removal of hedge funds into and out of the hedge fund index could avoid this.

Hedge Fund and Risk-free rate benchmark

Hedge Fund

Hedge Fund	Return	St. Dev.	Beta	Maximum drawdown (*1)	Sharpe ratio (rf=4%)	Risk
Long/short equity	14.6%	9.1%	0.1	-10.3%	(14.6%-4%)/9.1% = 1.16
Fixed income arbitrage	6.0%	4.1%	0.0 (*4)	-14.4% (*2)	(6.0%-4%)/4.1% = 0.49	Leverage risk Credit spread risk
Equity market neutral	8.1%	3.2%	0.6	-9.7%	(8.1%-4%)/3.2% = 1.28
Distressed securities	12.1%	5.6%	0.4	-12.8%	(12.1%-4%)/5.6% = 1.45 (*3)
S&P 500 index	10.4%	15.5%	-	-44.7%	(10.4%-4%)/15.5% = 0.41

(*1) The largest loss from peak to trough a hedge fund experienced over a certain period. Market disruption risk.

(*2)The greatest risk (of long-tail events) if a major market disruption were to occur.

(*3) Superior investment based on the highest Sharpe ratio, a hedge fund's risk-adjusted performance.

(*4) The positive risk-free rate benchmark (e.g. USD 1M LIBOR) can be justified by the fact that arbitrage strategies should be market neutral. It should be understood that the Equity Market Neutral hedge fund manager must take on some type of risk to generate excess returns.

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Risk-free rate benchmark

• The risk-free rate benchmark can be justified by the fact that arbitrage strategies should be market neutral. A market neutral fund should earn the risk-free rate. The Equity Market Neutral hedge fund employs a strategy that is closest to generate a return greater than the risk-free rate. It should be understood that the Equity Market Neutral hedge fund manager must take on some type of risk to generate excess returns.
• Both beta and correlation (to market index) in a question could be distractors. In practice, a market neutral fund's beta and correlation to the market index tend to be almost zero. (In the table above, Beta of Equity Market Neutral is 0.6 though.)

Swap

Swap

	Low(est)	Highest
Credit risk	At the end of the swap. (*1)	Generally highest in the middle of the swap.

(*1) There are few potential payments left, and the probability of either party defaulting on their commitment is relatively low.

Swap Spreads

Swap Spread = Swap rate (fixed-rate of an interest rate swap) - On-the-run Treasury yield(*)

(*) Treasury with the same maturity as the swap.

• An indicator for the general level of credit risk in the market.
• The fixed rate on any particular swap is the same for any interested party regardless of their credit quality.
• Therefore, the swap spread is a general measure of credit quality in the global economy.
• For example, if the fixed-rate of a 5-year swap is 7.26% and the 5-year Treasury is yielding at 6.43%, the swap spread is 7.26% - 6.43% = 83 bps.

Equity Swap

• A floating-rate (payer) equity swap
• Net value
• Zero on the reset date.
• Value of the floating side
• Par or
• Face value (e.g. $10 million)
• Replicating portfolio.
• Borrow money for the time to maturity at a floating rate
• Invest the proceeds in the underlying (e.g. equity index fund).

MBS

• An investor:
• wants to keep low interest rate sensitivity. (C1)
• wants to gain a substantially large OAS (option-adjusted spread) at a cheap price. (C2)
• is not concerned with credit risk.
• The term structure of interest rates is flat. (C3)

• (C1) A tranche with a low effective duration should be chosen.
• (C2) A cheap price → Low option cost, High OAS (*2)
• (C3) Z-spread = Nominal spread

MBS

MBS	Effective duration	OAS	Nominal spread	Option cost(*1)	OAS/Option cost
PAC Tranches
PT5	7.9 yrs	47 bps	62 bps	15 bps	3.13
Support Tranches
ST1	1.3 yrs (C1)	36 bps	60 bps	24 bps	1.50 (C2)
ST2	1.7 yrs (C1)	35 bps	69 bps	34 bps	1.03

(*1) Option cost = Z-spread - OAS; in this case, Z-spread = Nominal spread. (C3)
(*2) An investor who holds MBS with an embedded option does NOT actually receive an option cost (=premium). The investor gain only OAS (NOT z-spread) if option exercise is taken into consideration. So option costs should be lower, OAS should be higher.

Auto Loan ABS and Credit Card Receivable ABS

Auto Loan ABS and Credit Card Receivable ABS

	Auto Loan ABS	Credit Card Receivable ABS
ABS backed by	Amortizing assets (auto loan)	Nonamorzing assets (credit card receivable)
Collateral structure	Generally does NOT change once the security is issued. (*1)	Change during the lockout period. ("revolving structure") (*2)
Call provision (*3)		Usually included.
Prepayment rate of the ABS when interest rates ↑ or ↓	NOT significantly affected (*4)	NOT significantly affected (*5)

(*1) The collateral simply gets smaller as the loans are paid off by the borrower.

(*2) During the lockout period, principal payments on the collateral are used to purchase additional assets.

(*3) A call provision causes cash flows to be directed at principal reduction, rather than purchasing new collateral assets.
(e.g.) cleanup call : it is triggered by a decline in the value of the collateral.

(*4) Because autoloans 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 prepay the loan even if interest rates decline. Borrowers who take out an auto loan generally do not refinance their vehicles as interest rates decline.

(*5) During the lockout period, any principal payments (and prepayments) are used to purchase additional collateral for the ABS. Thus, any change in prepayment rates induced by interest rate changes would be offset by additional purchases of collateral. A contraction, or extension, 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))

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Selected Financial Data

Year		2008	2007	2006	2005	2004	2003	2002
EPS		(1.05)	1.90	1.65	0.99	1.35	0.77	1.04
BVPS		9.11	10.66	9.26	8.11	7.62	6.77	6.50
ROE		(0.115)	0.178	0.178	0.122	0.177	0.114	0.160

2008 EPS and ROE are left out of the estimates.

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Normalized EPS; the method of average EPS

	year & date	Sum	Average	Current
EPS	2002-2007	7.70 (*2)	7.70/6=1.28 (*1)
Stock price	12/31/2008			26.50
trailing P/E ratio	2008			26.50/1.28=20.70

(*1) Normalized EPS based on the method of average EPS
(*2) 1.90+1.65+0.99+1.35+0.77+1.04=7.70

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Normalized EPS; the method of average ROE

	year & date	Sum	Average	Current
ROE	2002-2007	0.929 (*3)	0.929/6=0.155
Normalized EPS	2008			Average ROE * BVPS2008 =0.155*9.11 =1.412
Stock price	12/31/2008			26.50
trailing P/E ratio	2008			26.50/1.412=18.768

(*3) 0.178+0.178+0.122+0.177+0.114+0.160=0.929

Emerging country firms

Emerging country firms

				Reason
estimated percentage of debt and equity		Estimated by a global industry index (*1)		(*2)
Beta		Industry beta for the firm's industry (*3) Beta against a well-diversified global index, NOT the local market index.

(*1) NOT the weights (calculated by the market value of the firm's debt and equity) for the firm.
(*2) Firms in emerging markets often use debt conservatively. So, Firms in the same industry in developed countries can have higher leverage ratios (e.g. Total assets / Total equity).
(*3) NOT an individual firm beta.

Emerging market valuation

Emerging market valuation

Adjustmement		Correct	Incorrect	Reason	Risk for foreign investors
Country risk		Cash flow	Discount rate (*2)	(*1)	(*3)

(*1) Companies within an emerging market will be affected differently by country risk. For example, exporters would benefit from a weaker local currency, but importors would be hurt by a depreciating local currency.
(*2) Adjusting the discount rate by the same amount for all companies within a country would misstate the influence of country risk on each company. See (*1).
(*3) Country risk for foreign investors may be greater than that for local investors. Country risk is asymmetric 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 to adjust the discount rate.

Nominal forecasts of firm performance under a high inflation

Nominal forecasts of firm performance under a high inflation

			Nominal
Return on invested capital		NI / (D+E)	NI↑ / (D+E) ; ↑ : overstated
Net working capital to revenues		NWC / Revenue	NWC↑ / Revenue↑ ; correctly estimated with either real or nominal projections.
Net property plant and equipment to revenues		Net PP&E / Revenues	Net PP&E / Revenue↑ ; understated

Residual Dividend Model and Residual Dividend Policy (Plan)

Residual Dividend Model

Capital Structure
Debt			40%
Equity			60%
Income Statement items
Estimated net income (also retained earnings)		at the end of current year	$153 million
Fund raising for the planned net instments
Planned net investments		In the current year	$160 million
Fund raised		by debt	160*40%=$64 millon
Fund raised		by equity (retained earnings)	160*60%=$96 millon
Retained earnings
Net investments			$96 millon
Dividends		(residual after the net investments)	153-96=$57 million
Dividend payout ratio			57 / 153 = 37.25%

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Residual Dividend Policy (Plan)

1. A firm determines the optimal capital budget.
2. Uses retained earnings to fund the optimal capital budget, paying out what is left over to shareholders.
3. Because the amount of distributable earnings is not known in advance and is determined as a function of the capital budget, the dollar dividend paid to shareholders will fluctuate widely from year to year.
4. However, the firm will be able to use internally generated funds to a greater extent when deciding how to fund the optimal capital budget.
5. It is NOT true, however, that the redisual dividend policy will reduce the firm's cost of capital. Investors do not like unpredictable dividends and will penalize the company in the form of a higher required return on equity to compensate for the additional uncertainty related to dividend payments.

Birds-in-the-hand theory

Birds-in-the-hand theory

			Investors perception
Investors preference in Capital gain or Income gain?			Income gain would be preferable. (*2)
Dividends paid by a company		Instable	Negative(*1)
Stock price		Punished
Cost of equity		Higher
Equity value		Lower
Stock repurchase			Unpredictable and possibly one-time event. (*3)

(*1) Any volatility (both increase and decrease) in dividends is seen as a negative sign by investors.
(*2) Uncertainty associated with capital appreciation vs. relative certainty of dividends.
(*3) A repurchase does not provide the same type of assurance since it is an unpredictable and possibly one-time event.

ex-dividend: change in the stock price when the stock goes ex-dividend

|Δp| * (1-T_CG) = D * (1-T_D)
|Δp| = D * (1-T_D)/(1-T_CG)


|Δp| : the change in the stock price when the stock goes ex-dividend (in absolute terms, since Δp < 0)
D: dividend declared per share
T_D : tax bracket for dividends
T_CG : tax bracket for capital gains

(e.g.)
D = 2.25
T_D = 15%
T_CG = 39.6%

|Δp| * (1 - T_CG) = D * (1 - T_D)
|Δp| = D * (1 - T_D) / (1 - T_CG)
= 2.25 * (1 - 15%) / (1 - 39.6%) = 3.1664... ≈ 3.17

Target Payout Ratio Adjustment Model Approach (Target Payout Ratio Approach)

ΔDividends = ΔEarnings * Target Payout Ratio * Adjustment Factor
Target Payout Ratio = ΔDividends / (ΔEarnings * Adjustment Factor)

Adjustment Factor = 1 / t
t: number of periods (e.g. year) to meet a target payout ratio

Target Payout Ratio Adjustment Model Approach (Target Payout Ratio Approach)

Dividends-increasing period			8 years
Adjustment factor			1/8=0.125
Earnings	(t=0)		$ 145 * 10^6
Earnings	(t=1, expected)		$ 153 * 10^6
ΔEarnings	(from t=0 to 1, expected)		$ 8,000,000
ΔDividends	(from t=0 to 1, expected)		$ 250,000

Target Payout Ratio = ΔDividends / (ΔEarnings * (1/t)) = 250,000 / (8,000,000 * 0.125) = 25%

PBO under U.S. GAAP and IFRS

PBO under U.S. GAAP and IFRS

	U.S. GAAP		IFRS
Unamortized past service cost	37	→	Eliminated from the funded status
PBO (*)	635		635-37= 598; Lower (**)
Funded status	-240		-240-(-37)= -203 (↑, higher than U.S. GAAP)

(*) Pension liability on the B/S

(**)
Funded status = Plan assets - PBO
PBO = Plan assets - Funded status
So,
PBO ↓ = Plan assets - Funded status ↑

Fair market value of plan assets

Fair market value of plan assets_Y-1 + Contribution to pension plan_Y - Benefits paid_Y + Actual return on plan assets_Y = Fair market value of plan assets_Y

Y: year

Capitalized cash flow method, Excess earnings method, and Free cash flow method

Capitalized cash flow method, Excess earnings method, and Free cash flow method

Name		Growth	Intangible assets to value?
Free cash flow method		Two-stage
Excess earnings method			Yes
Capitalized cash flow method		Single-stage (constant growth)

Financial Transaction and Strategic Transaction

• Strategic transaction
• A target firm is acquired based in part on the synergies it brings to the acquirer.
• Financial transaction
• It occurs when there are no synergies.
• A acquiring firm does not own a company in the same industry with the target's; so acquiring firm cannot merge the target company with another company, i.e. no synergies.

Currency, Current Account, and Capital Account

Unexpected decrease in the budget deficit of U.S. government

Economy		↓ (slowdown)
Inflation		↓
Imports		↓
Exports		↑
USD		↑ (appreciation)
Government borrowing		↓
Real interest rates		↓
Investment funds		flow out of the U.S.
USD		↓ (depreciation)	(*)
Aggreate demand		↓
Imports		↓
Current account deficit (Trade deficit)		↓	(***)
Domestic (U.S.) interest rates		↓	(**)
Foreign investment in the U.S.		↓
Domestic capital invested in foreifn countries		↑
Capital account surplus		↓

(*) 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.
(***) Current account; balance of trade = exports - imports (of goods and services)

Currency: demand-supply analysis, interest rates and equilibrium quantity

Currency: demand-supply analysis, interest rates and equilibrium quantity

			FC/DC	Equilibrium quantity
DC	Nominal interest rates	↑
DC	Demand	↑ (1)	↑ (DC appreciates)	↑ (1)
DC	Supply	↓ (2)	↑ (DC appreciates)	↓ (2)
	Net effect		↑ (DC appreciates)	NOT significantly affected.

(1) Damand for DC increases to capitalize on the higher interest rate return.
(2) Supply for DC decreases since the current DC holder would like to keep it to get higher interest rate return.

Real Exchange Rate

Nominal Exchange Rate (GBP/CAD) = Real Exchange Rate (GBP/CAD) * (P_GBP/P_CAD)
or
Real Exchange Rate (GBP/CAD) = Nominal Exchange Rate (GBP/CAD) * (P_CAD/P_GBP)

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(e.g.)

• Nominal Exchange Rate (GBP/CAD) = 0.40 (GBP/CAD)
• The ratio of the price of the U.K. consumption basket to the Canadian consumption basket = (P_GBP/P_CAD)_t=0 = 0.3

∴Real Exchange Rate (GBP/CAD) = 0.40 * (1/0.3) = 1.33

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(e.g.)

• Real exchange rate remained constant.
• (GBP/CAD)_{Real, t=1yr} = (GBP/CAD)_{Real, t=0}
• (GBP/CAD)_{Real, t=0} = (GBP/CAD)_{Nominal, t=0} *  (P_CAD/P_GBP)_t=0
• (GBP/CAD)_{Real, t=1yr} = (GBP/CAD)_{Nominal, t=1yr} * (P_CAD/P_GBP)_t=1 = (GBP/CAD)_{Nominal, t=1yr} * (P_CAD/P_GBP)_t=0 * (1+i_CAD)/(1+i_GBP)
• ∴(GBP/CAD)_{Nominal, t=1yr}  = (GBP/CAD)_{Nominal, t=0} * (1+i_GBP)/(1+i_CAD) (exact version)
• ∴(GBP/CAD)_{Nominal, t=1yr} = (GBP/CAD)_{Nominal, t=0} * (1+i_GBP - i_CAD) (approximate version)
• i_GBP = 4%
• i_CAD = 7%

∴GBP return on the Canadian stock
=CAD Total return - (i_CAD - i_GBP) =CAD Total return + (i_GBP - i_CAD)
= 22% - (7% - 4%) = = 22% + (4% - 7%) = 19%

i_CAD - i_GBP = 7% - 4% = 3%
CAD depreciates by 3%. GBP appreciates by 3%.

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(e.g.)

• Real exchange rate changed.
• (GBP/CAD)_{Real, t=0} = 1.33
• (GBP/CAD)_{Real, t=1yr} = 1.41
• A Canadian stock's 1 year total return = 22%.
• i_GBP = 4%
• i_CAD = 7%

(GBP/CAD)_{Nominal, t=1yr}
= (GBP/CAD)_{Real, t=1yr} * (P_GBP/P_CAD)_t=1yr
= (GBP/CAD)_{Real, t=1yr} * (P_GBP/P_CAD)_t=0 * (1+i_GBP)/(1+i_CAD)
= 1.41 * 0.30 * (1+4%)/(1+7%)
≈ 0.41114

GBP appreciated while CAD depreciated.

∴GBP total return
= CAD total return + CAD appreciation
= 22% + (0.41114-0.40)/0.40
= 22% + 2.785% = 24.785%

Merger: Takeover Premium (Gain for the Target company's shareholders)

• Synergies from the acquisition = 600 = S
• Stock exchange ratio
• Acquirer 0.75 share : Target company 1 share (*1)
• No cash is changing hands for the merger.

Merger

Pre-merger	Acquirer	Acquirer's new issue for the merger	Target company
Stock price	$ 60	$ 60	$ 39
Shares outstanding	150	60 (*1)	80
Market value	$ 9,000 = VA	$ 3,600	$ 3,120 = VT

Post merger value of the combined firm:
V_AT = V_A + V_T + S - C = 9,000 + 3,120 + 600 - 0 = $ 12,720

Price per share of the combined firm
P_AT = V_AT / (S_A + S_{A, new share}) = $ 12,720 / (150 + 60) = $ 60.57

Actual price paid for the Target company
N * P_AT = 60 * $ 60.57 = $ 3,634.2

Target company's gain as the target
_GainT =(N * P_AT) - V_T = $ 3,634.2 - $ 3,120 = 514.2 (takeover premium in the transaction)

Merger Transaction

Acquisition: Form of integration

Potential target company	Optimal form of acquisition	Method of payment	Attitude of target
B	Purchase of the target's 30% assets	Cash offering	friendly
C	Stock purchase	Securities offering	friendly
D	Stock purchase	Mixed cash and securities offering	hostile
E	Stock purchase	Cash offering	friendly

(Question)
Which of the following statements concerning the transaction characteristics of the potential mergers with an acquiring company A is most appropriate?

A. Purchasing E is most likely to reduce A's financial leverage.
B. C would like to avoid paying corporate taxes in the potential deal with A.
C. B's shareholders would likely be required to approve the deal with A before any proposed deal is completed.

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Answer: B

The acquisiton of C is described as a stock purchase, which means that C's shareholders would be needed to pay capital gain taxes on the deal and no taxes would be levied against C at the corporate level.

The deal with E is desribed as a cash offering. In most cash offerings, the acquirer borrows money to raise cash for the deal, which would increase the acquirer's financial leverage.

In the deal with B, shareholders generally only approve asset purchases when the purchase is substantial (greater than 50% of firm assets).

(FYI)
In a proxy battle for D, A would try to have shareholders approve new members of the board of directors to try to gain control of the company. Trying to purchase shares from shareholders individually is a tender offer.

Acquisition: Form of integration & Type of merger

Acquisition: Form of integration

Form of integration
Subsidiary		Maintain the successful target company's brand and operational structure. Most subsidiary mergers occur when the target has a well-known brand that the acquirer wants to maintain.
Statutory		The target company would cease to exisit as a separte entity.

Acquisition: Type of merger

Type of merger
Horizontal		An acquirer and a target company are in the same industry.
Vertical		An acquirer would be moving up or down the supply chain.

High Inflationary Environment

A U.S. company's subsidiary is operating in a highly inflationary environment. Treatments in U.S. GAAP and IFRS (for comparison) are as follows:

High Inflationary Environment

Foreign subsidiary's :	U.S. GAAP	IFRS
Nonmonetary assets	NOT restated for inflation	Adjusted for inflation
Nonmonetary liabilities	NOT restated for inflation	Adjusted for inflation
Financial statements		Adjusted for inflation
Net purchasing power gain or loss		Recognized in I/S. The subsidiary is translated in USD using the current rate method.
Foreign currency translation	Temporal method	Current rate method
Foreign currency adjustment gain or loss is recognized in:	I/S	B/S

Foreign Currency Translation Adjustment under Current Rate Method and U.S. GAAP

• Current Rate Method
• U.S. GAAP

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• A parent company is a U.S. company.
• A foreign subsidiary is self-contained, independent company in Switzerland.
• Current Rate Method
• Translation gain/loss is reported on B/S.
• Also, as a pre-condition,
• Taxes paid = 0
• Dividends paid = 0
• Inventory: FIFO

Exchange Rate

Date	USD/CHF
1/1/2008 (*1)	0.77
12/31/2008	0.85
Average 2008	0.80

(*1) A subsidiary in Switzerland was established.

I/S of foreign subsidiary for 2008

(in CHF)	CHF	USD/CHF	USD
Sales	7,000	A 0.80	5,600
COGS	-6,800	A 0.80	-5,440
Depreciation	-100	A 0.80	-80
Net income	100	A 0.80	80

B/S of foreign subsidiary as of 12/31/2008

	CHF	USD/CHF	USD
Assets
Cash and accounts receivable	600	C 0.85	510
Inventory	500	C 0.85	425
PP & E	600	C 0.85	510
Total assets	1,700	C 0.85	1,445
Liabilities and equity
Account payable	200	C 0.85	170
Long-term debt	100	C 0.85	85
Common stock	1,300	H 0.77	1,001
Retained earnings	100		(*2) 80
Foreign currency translation adjustment			(*4) 109
Total liabilities and owner's equity	1,700		(*3) 1,445

(*2) Retained earnings = Beginning retained earnings (H) + Translated net income (A) - Dividends paid (H)
= 0 + 80 (from I/S) - 0 = 80
(*3) Should be the same as Total assets to balance.
(*4) 1,445 - (170+85+1,001+80) = 109

Acquisition, Equity, and Proportionate consolidation method

Accounting treatment

method	equity		proportionate consolidation		acquisition
IFRS	OK: Allowed		OK: Preferred		OK
U.S. GAAP	OK		Generally NOT allowed (*)		OK
Net income	+share(%)	=	+share(%)	<	+100(%)
Total liabilities	-	<	+share(%)	<	+100(%)
Total assets	-	<	+share(%)	<	+100(%)
ROA		>		?

(*) Proportionate consolidation is not allowed except in very limited situations.

Acquisition method and Equity method (U.S. GAAP)

(Case) A U.S. company's 45% ownership stake in another U.S. company:

Accounting treatment (U.S. GAAP)

method	equity		acquisition
Net income	+share(%)	<	+100(%)
Total asset	-	<	+share(%)
ROA		>, <, or =

Economic Pension Expense

Economic Pension Expense

	2008	2007
Net pension cost (*1)	7,704
service cost	8,298
interest cost	4,128
actuarial loss (gain, if negative)	-1,932
actual return (positive return, if negative)	-7,084
economic pension expense (*2)	3,410
plan assets
funded status	2,524	934
Employer contributions	5,000

(*1) AKA reported pension expense
(*2) Economic pension expense = Service cost + Interest cost + Actuarial loss - Actual return on plan assets
= 8,298 + 4,128 -1,932 - 7,084 = 3,410

Alternatively,
Economic pension expense =  Employer Contributions(*) - Δfunded status
= 5,000 - (2,524 - 934) = 3,410

(*) Participant(=Employee) contribution is NOT included.

∴ economic pension expense (3,410) < reported pension expense (7,704)

Furtheremore,
Economic pension expense =  Benefits paid + ΔPBO - Actual return on plan assets

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Economic Pension Expense

	2008	2007
economic pension expense	4,250
plan assets
funded status	2,524	934
Employer contributions	5,000
CFO adjustment	+750
CFI adjustment	0
CFF adjustment	-750

Note:

• Ignore income taxes.
• Economic pension expense represents the true cost of the pension. If the firm's
• employer contributions > economic pension expense
• employer contributions (CFO) - economic pension expense = 5,000 - 4,250 = 750
• viewed as a reduction in the overall pension obligation similar to an excess principal payment on a loan (CFF).

Pension accounting

Pension accounting

discount rate	↑
life expectancy		↑
rate of compensation			↓
expected return on plan assets				↑
PBO (*1)	↓		↓	-
ABO (*2)			-
service cost	↓		↓
interest cost	?(*3)
pension expense	↓		↓	↓
plan assets			-
funded status	↑		↑	-
net income	↑		↑	↑
retained earnings	↑		↑	↑
Actuarial gain/loss	gain	loss

(*1) PBO: Pension (or Projected) Benefit Obligation
(*2) ABO: Accumulated Benefit Obligation
(*3) Interest cost cannot be determined without more information.

Net Pension Assets: adopt U.S. pension accounting standards instead of IFRS

Net Pension Assets: adopt U.S. pension accounting standards instead of IFRS

	IFRS	(*3)	U.S. GAAP (*2)
Net pension asset (*1)	7,222
Funded status		→	2,524
ΔAsset (adjustment)			-4,698 (*4)
ΔEquity (adjustment)			-4,698 (*5)

(*1) Net pension asset = Funded status + Unrecognized transition asset + Unrecognized prior service cost + Unrecognized net actuarial loss

(*2) assuming no taxes

(*3) adopt U.S. pension accounting standards

(*4) 2,524 - 7,222 = -4,698
(*5) in order for the accounting equation to balance

Earnings Quality

Earnings Quality

	Sample case	Reasoning	Earnings Quality
Discretionary expenses	Discretionary expense items are declining as the: Investment in capital assets ↑ (∵CFIt > depreciationt) Sales ↑	Doubt about manipulation.	Low
Depreciation method	Changed from the double-declining balance method to the straight-line method. This is aimed at being more comparable with the accounting practices of other firms within the industry. The change was not retroactively applied and only affects assets that were acquired on or after a certain specified date.	Measuring earnings quality based on conservative earnings (with double-declining balance method) is inferior measure as most accruals will correct over time.	Higher under the straight-line method than the double-declining method.
Inventory/COGS	LIFO Under stable or rising prices.	It would cause net earnings to reflect economic (real) earnings.	Higher
Lease	Finance (capital) lease	A finance lease is reported on the B/S as an asset and as a liability. In the I/S, the leased asset is depreciated and interest expense is recognized on the liability.	Higher (than operating lease).
Receivable sale	Receivable sale with recourse	CFO ↑ However, the receivable sale is a collateralized borrowing arrangement that remains off-balance-sheet.	Lower

Revenue: recognizing revenue too soon

From a certain company's financial footnotes:
Sales are recognized when a firm order is received from the customer, the sales price is fixed and determinable, and collectibility is reasonably assured.

---

Revenue should be recognized when earned and payment is assured. Since the company still has an obligation to deliver the goods, revenue is not yet earned. By recognizing revenue too soon,

Revenue: recognizing revenue too soon

		by recognizing revenue too soon
Net income		overstated
Ending inventory		understated
Inventory turnover	= Revenue / Inventory	= (overstated)/(understated) = overstated

APT and CAPM

The APT is a better approach than the CAPM because even though the factor risk premiums are difficult to estimate, the CAPM is more problematic because it relies on a single market risk premium estimate, which in turn leads to greater input uncertainty.

Incorrect.


From a purely theoretical point of view, one cannot say that the APT is better than the CAPM because the CAPM relies on a single market risk premium. If anything, due to the greater number of inputs required in APT estimation, input uncertainty is probably a more significant problem for the APT than it is for the CAPM.

Convexity

Convexity = (V_- + V₊ - 2V₀)/(2 * V₀ * Δy²)

V_-: bond value when the yield decreases by Δy
V₊: bond value when the yield increases by Δy
V₀: original bond value
Δy : absolute change of yield

OAS and Z-spread

Z-spread and OAS

	Straight corporate bond	Callable corporate bonds	Home equity loan ABS
embedded option?	No	Yes	Yes
Cash flows are interest path dependent?	No	No	Yes
most appropriate spread measure	Z-spread	OAS from binominal model	OAS from Monte Carlo model

Amortizing asset and Non-amortizing asset

Amortizing asset and Non-amortizing asset

	example	composition of the loans in the asset pool
Amortizing asset	auto loan	does NOT change
Non-amortizing asset	credit card receivable	does change

CMO: support tranche, PAC I tranche, and effective collar

Table

PSA speed	Tranche XX	Tranche YY
0	21.9	12.2
50	17.5	8.9
100	13.2	5.1
150	9.1	5.1
200	4.3	5.1
250	3.6	5.1
300	2.9	5.1
350	2.0	4.7
400	1.4	3.9
	support	PAC I
prepayment risk (*)	higher	lower
effective collar		100-300 PSA (**)

(*) as measured by the average life valiability
(**) the range of prepayment speeds over which the average life of the tranche is constant.

FRA: current value

Table

	LIBOR spot
Days	Day=0	Day=30
30	3.12%
60	3.32%
90	3.52%
120	3.72%	3.92%
150	3.92%
180	4.12%

---

2x5 FRA (Day=0)
= ((1+3.92%*(150/360))/(1+3.32%*(60/360))-1)*(360/90) = 4.30%
↓
1x4 FRA (Day=30)
= 4.14% (given)

---

(1) Day=0
Short 2x5 FRA

(2) Day=30
The current value of the $10 million FRA to the short position. (short FRA: Pay - floating, Receive - fixed)

(10*10^6)*(4.30%-4.14%)*90/360/(1+3.92%*120/360) = $3,948

Forward contracts on a Treasury bond

Table

Forward	maturity	270 days
Treasury	maturity	10 years
	coupon	5% (*)
	(dirty) price	98.25
Risk-free rate		4% (**)

(*) It has just made a coupon payment; next two coupon payments will be in 182 days and in 365 days.
(**) Effective annual risk-free rate.

---

[1] No-arbitrage price for the forward contract on the Treasury bond

Table

Days	coupon (per $100 face value)	Treasury	No-arbitrage forward price
0	(1) PV = 2.50/1.04^(182/365)	98.25	(2) 98.25 - 2.50/1.04^(182/365)
182	100*5%*(1/2) = 2.50
270			(3) (98.25 - 2.50/1.04^(182/365))*1.04^(270/365) = 98.62

---

[2] If the Treasuary bond dirty price decreases to 98.11 over the next 60 days, the value of a short position in the 270-day forward contract on a $10 million bond is:

Table

Days	coupon (per $100 face value)	Treasury	No-arbitrage forward price
0
60	(1) PV = 2.50/1.04^(122/365)	98.11	(2) 98.11 - 2.50/1.04^(122/365)
182	100*5%*(1/2) = 2.50
270

(3) The value of the forward contract to the long:
98.11 - 2.50/1.04^(122/365) - 98.62(answer in [1])/1.04^(210/365) = -0.77693 per $100
∴-$77,693


short: +0.77693 per $100
∴+$77,693

Treynor-Black model: modifying a Treynor-Black model to account for an analyst's forecast error

Modifying a Treynor-Black model to account for a lack of precision in an analyst's forecast is most likely to include:

A. a correction to the analyst's forecast of alphas based on their prior bias.
B. adjusting the Treynor-Black actively managed portfolio weights using the square of the correlation between the analyst's forecast and realized alphas.
C. reducing portfolio weights by the reciprocal of the analyst's average alpha forecast error as a percentage of expected excess returns.


Answer: B

---

An analyst's forecasting ability can be judged based on past performance. The Treynor-Black weightings within actively managed portfolios can be adjusted based on an analyst's prior forecasting ability. The process is to:

• Collect the time-series alpha forecasts for the analyst.
• Calculate the correlation between the alpha forecasts and the realized alphas.
• Square the correlation to derive the R².
• Adjust (shrink) a forecast alpha by multiplying it by the analyst's R².

Tracking Portfolio

The information ratio for a tracking portfolio is:

A. expected to be zero.
B. an indicator of a manager's systematic risk exposure.
C. an indicator of a manager's pure stock selection ability.


Answer: C

---

A tracking portfolio is designed to have the same systematic risk as the benchmark. Hence, any difference in portfolio versus benchmark returns comes from security selection.

Treynor-Black model: optimal portfolio

(Question)
The optimal portfolio for an investor under the Treynor-Black model:

A. depends on analyst forecast accuracy.
B. depends on the unsystematic risk of mispriced securities.
C. is not sensitive to a change in the risk-free rate of interest.


Answer: B

---

• While the Treynor-Black model can be modified to include analyst forecast accuracy in the calculation of active portfolio weights, this is NOT part of the model itself.
• The unsystematic risk of securities in the active portfolio is an important input into the information ratio and active portfolio weights.
• A change in the risk-free rate can be expected to change an investor's allocation between the risk-free asset and the optimal risky portfolio and will change the estimates of abnormal returns (alpha) for active portfolio stocks, and, thereby, their portfolio weights.

VaR (Value at Risk)

Value at Risk have several limitations as a risk measurement tool.

(Question)
The least appropriate limitation of value at risk (VaR) as a risk measurement tool for hedge fund is that:

A. VaR does not provide a left tail risk value.
B. hedge funds often use derivatives, causing their return distributions to be skewed.
C. VaR provides no information on the magnitude of loss beyond the minimum loss.


Answer: A

VaR as a measure of risk in hedge funds has several limitations. VaR, for example, assumes a normal distribution of returns. Therefore, it is not useful for measuring risk in strategies that are negatively skewed or using derivatives, which typically have non-normal returns distributions (think of options, for example). VaR also only indicates the minimum loss at a given level of significance but gives an analyst no information on potential losses beyond this minimum amount.

By definition, VaR gives information on the left tail risk value, for a given probability of occurrence and the time interval.

---

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

Risk-free rate as an appropriate risk measure in hedge fund performance evaluation

(Question)
Even in market neutral strategies, the risk-free rate may not be an appropriate measure of fund performance. Because:

A. the risk-free rate is not an appropriate risk measure because it ignores the systematic risk.
B. the risk-free rate is not an appropriate risk measure because the market neutral strategy does not always have a zero beta risk exposure.
C. the risk-free rate is not an appropriate risk measure because leverage in a market neutral strategy magnifies risk.


Answer: B

The risk-free rate argument rests on the assumption that a market-neutral strategy is risk-free due to zero beta exposure. However, even zero beta market-neutral hedge funds are not truly risk-free because there is no argument on what constitutes the "market."

Market-neutral strategies are often poorly diversified and hence may still contain significant unsystematic risk (not systematic risk).

Leverage magnifies risk in a fixed income arbitrage fund and not a market neutral fund.

Fixed Income Arbitrage

Fixed Income Arbitrage

market/economy		↓(downturn)	↑(booming)
High-credit-risk bond	yield	↓	↑
Treasuries	yield	↓ ↓	↑ ↑
Net:	credit spread	↑(widening)	↓(tightening)
Long: High-credit-risk bond	P&L	+ (profit)	- (loss)
Short: Treasuries	P&L	-- (loss)	++(profit)
Net position		- (loss)	+ (profit)

Put option

Put option

Underlying	↓	↑
Put option: Intrinsic value	↑
Put option: Time value		↑
Put option: total value	↑(generally)(ITM)	(OTM)

EVA, Invested Capital, and NPV

NPV, Invested Capital, and EVA

	a startup company
NPV	Positive (given)
Invested capital	↑(=when increasing invested capital)
NOPAT	↑(*2) ↑
$WACC	↑(*2)
EVA = Economic profit (*1)	↑

(*1) EVA = Economic Profit = NOPAT - $WACC
(*2) The increase in NOPAT will be larger than the increase in $WACC, so EVA will increase.

Standard error: use of standard errors in a regression to correct for serial correlation

(Sample Case)
An analyst observes that two reputable statistical analysis firms estimate betas for a company A stock at 0.85 and 1.10. He concluded that the differences between his beta estimate and the published estimates resulted from his use of standard errors to correct for serial correlation; the other firms did not make a similar adjustment.


False
Using adjusted standard errors will change the t-statistics and potentially the statistical significance, but not the beta estimate itself.

FCFE coverage ratio

FCFE coverage ratio = FCFE / (Dividends paid + Share repurchase)

Market Portfolio

• Sharpe ratio
• Assuming all investors agree on all asset return, variance, and correlation expectations, then the market portfolio has the highest Sharpe ratio.
• (E(R_M) - R_f)/σ_M > (E(R_p) - R_f)/σ_p

Covaricence Stationary

NOT covariance stationary

• Features
• The mean of the data (e.g. X: time, Y: price) is not constant.
• AR(1): X_t = b₀ + b₁*X_t-1 → b₁≅1
• Test
• Dickey-Fuller test
• H₀ : b₁ - 1 = 0
• If H₀ is not rejected, data has a unit root and is nonstationary.

NPV venture capital method

NPV venture capital method

Year	Capital invested ($ million)	Selling price ($ million)	Discount rate	Pre-money valuation	Post-money valuation
0	-20 (*)				(3) 1/(1+40%)^4*(+400/(1+30%)^2 - 40) = 51.1991
1			40%
2			40%
3			40%
4	-40		40%	(2) +400/(1+30%)^2 - 40	(1) +400/(1+30%)^2
5			30%
6		+400	30%

(*) capital investment today by the first-round investors


Fractional ownership for first-round investors:
f₁ = INV₀/POST₀ = 20/51.1991 = 39.06%

S_pe: number of shares owned by the private equity LPs (first-round investors)
S_e: number of shares owned by a company(investee;investment target)'s founders = 5 million shares

(S_pe+S_e)*f₁ = S_pe
S_e*f₁ = S_pe * (1-f₁)
S_pe = S_e*f₁/(1-f₁)
= 5,000,000*39.06%/(1-39.06%) = 3,204,792 shares


Stock price after the first round of financing
P₁
= POST₀/(S_pe+S_e)
= 51.1991*10^6/(3,204,792+5,000,000)
= INV₀/S_pe
= 20*10^6/3,204,792
= $6.24

Private equity & Venture capital : Carried interest, Tag-along, drag-along clause, Ratchet, and Distribution waterfall

Private equity & Venture capital : Carried interest, Tag-along, drag-along clause, Ratchet, and Distribution waterfall

term	description
Carried interest	GP's share in fund's profits, generally set at 20% of net profits after fees.
Tag-along, drag-along clause	Management (generally mininority shareholder)'s right to sell their equity interest in the event of an acquisition. A contractual obligation used to protect a minority shareholder. If a majority shareholder (e.g. a private equity owner) sells his or her stake, then the minority shareholder has the right to join the transaction and sell (or buy) his or her minority stake in the company. It requires a future acquirer to make an offer for all shares before taking control. "A private equity fund will reorganize each company it acquires so that a future acquirer cannot take control without extending a purchase offer to all-shareholders, including current management." Also referred to as "co-sale rights".
Ratchet	Specifying the equity allocation between the limited partners (LPs, i.e. private equity fund investors) and management.
Distribution waterfall	Specifying how profits will flow to the LPs and also the conditions under which the GP may receive carried interest.

Equity valuation: DCF method, Relative value approach, and Venture capital method

Equity valuation: DCF method, Relative value approach, and Venture capital method

	a startup company	a company and its industry with a long history
DCF method	less appropriate (*1)	appropriate
Relative value approach	less appropriate (*2)	appropriate
Venture capital method	appropriate

(*1) It would be difficult to assess its future cash flows.
(*2) There are likely few comparables to benchmark against.

General Partner(GP) (of a private equity fund)

General Partner(GP) (of a private equity fund) = A fund manager of the fund


→ the fund's investor = limited partner

Earnings Yield

Earnings Yield = Earnings per share for the most recent 12-month period divided / Current market price per share

The earnings yield is the inverse of the P/E ratio.