Information Ratio

IR = (IC) * (BR)^0.5

Information Ratio = (Information Coefficient) * (Breadth)^0.5

Information Coefficient : depth of knowledge (correlation between the manager's forecasted and actual returns)

Breadth : number of independent investment decisions (e.g., # of index constituents)

Passive Fund Construction Strategies: characteristic of the index and fund

Passive Fund Construction Strategies: characteristic of the index and fund

Index / Fund	factors to consider when choosing a strategy	Full Replication	Stratified Sampling or Optimization
Index	# of stocks	Few (limited)	Large
Index	Liquidity	High	Illiquid (at least some of index constituents are illiquid)
Fund	Cash (as funds to invest)	Significant (huge)
Fund	Tracking Error (as a result of portfolio construction)	Low	Relatively higher (compared to Full Replication)
Fund	Rebalancing when	Index stock change Cash inflow / outflow (including dividends)

Rebalancing: Strategy, Factors, and Corridor

Rebalancing: Strategy

Rebalancing: Strategy	Constant Mix	Constant Proportion (e.g., CPPI)	Buy and Hold
Optimal for investors with a floor value?		a floor value which limits his or her willingness to take risks if one's portfolio declines below that value	floor value >= 0
Optimal for investors with absolute risk tolerance that:	varies proportionately with wealth 0 < one's multiplier < 1	varies by more than any change in one's wealth  one's multiplier > 1	one's multiplier = 1
GOOD performance if markets are	Ups and downs (mean-reversion, or "volatile" markets)	Trending (with no or few reversals)	in the middle of Constant Mix and Constant Proportion
POOR performance if markets are	Trending (with no or few reversals)	Ups and downs	in the middle of Constant Mix and Constant Proportion
Payoff Curve	Concave (*1)	Convex	Linear

Also, Calendar Strategy's Rebalancing Frequency depends on volatility of asset class in the portfolio.

(*1) It supplies liquidity to the market, in effect "selling insurance" by taking the less popular side of trades when the market is trending up or down.

Rebalancing: Factors

#	Factor
1	Volatility	High		Low
2	Frequency	Infrequent	Appropriately frequent	Too frequent
	Market Impact / Trading Cost	High Asset mix can drift to the point where rebalancing could create a market impact, thus increasing the cost of trading dramatically.	Low Market impact will be lower with more frequent rebalancing.	High Portfolio could incur numerous costly small trades to achieve minor adjustments in the asset mix.

Rebalancing: Corridor

#
1	Risk tolerance		High
2	Flexibility for the asset allocation relative to the target mix		High
3	Volatility			Low	High
4	Correlation with the rest of the portfolio			High	Low
5	Transaction Cost			High	Low
	Rebalancing Corridor Width		Wide	Wide	Narrow (*2)

(*2) The narrow corridor means that small changes in value may necessitate rebalancing.

Concentrated Position in a Publicly Traded Common Stock

Concentrated Position in a Publicly Traded Common Stock

#				Consequence
1	Outright Sale			Significant tax liabilities
2	Monetization			It provides the owners with funds to spend or reinvest without triggering a taxable event. (e.g.,) a loan against the value of a concentrated position
3	Hedging			Use of derivatives (e.g.,) a long put

Goal-based Planning

Goal-based Planning

Risk Bucket		Personal	Market	Aspirational
Goal		Protection from poverty or a decrease in lifestyle	To maintain the current standard of living	Opportunity to increase wealth sustainability
Examples of investment instruments		Personal residence Certificate of Deposit (CD) Treasury securities Other safe investments	Stocks Bonds	Privately owned business Commercial and investment real estate Concentrated stock positions

Hedging Strategies

Hedging Strategies

			Pros	Cons
Hedging with futures			Typically greater liquidity than options No cost to enter No requirement for frequent adjusting /rebalancing	Forgoes any potential appreciation in hedged instrument(s) More distant (in price) contracts increase basis risk More distant (in price) contracts are less liquid
Insuring with options (Option insurance strategy)			Offer upside gain while hedging downside losses	Initial outlay of option premium requirement Option premium crea an imperfect hedge
Delta hedging with options			Opportunity to capture upside gains, if they occur More closely hedge the exposure (than the option insurance strategy)	Constant rebalancing requirement Expensive transaction costs because of frequent rebalancing

Expected Annual Return of the Equity Index

Expected Annual Return of the Equity Index

E(R_d)
= (Dividend Yield) + {Capital Appreciation or Depreciation}
= (D/P) - (ΔS) + i + g + (ΔP/E)

(D/P) = Dividend Yield

(ΔS) = % Change in Shares Outstanding (positive when share issuance, negative when share repurchases occur)
i = Inflation Rate
g = Real Earnings Growth
(ΔP/E) = Repricing as economic activity is expected to accelerate in the next 12 months (*)

(*) Repricing refers to changes in nominal earnings multiplier (price/earnings ratio) that determines the share's market price. P/E ratios typically expand as the economy expands and contract as the economy contracts, although not necessarily at the same pace or precisely in sync with each other.

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For instance,

(D/P) = 1.25%

(ΔS) = -1.50% (shares REPURCHASE % of outstanding shares)

i = 2.50%

g = 3.50%

(ΔP/E) = 4.00%

 E(R_d) = (D/P) - (ΔS) + i + g + (ΔP/E) = (1.25) - (-1.50) + 2.50 + 3.50 + (4.00) = 12.75%

GIPS-comliant Performance Reporting

GIPS-compliant Performance Reporting

#		GIPS Requirement	Non-GIPS-Compliant
1	Total Return	Total Return = (Price Return) + (Income Return) - (Actual Incurred Trading Expenses) (*1)	Estimated Trading Expenses
2	Minimum Asset Level	Disclosure
2	Material Changes in Calculation Methodology	Disclosure (*1)
4	Real Estate	Internal (in-house) Valuation: at least Quarterly (Jan 1, 2008 -) External Valuation: Every Year (as of Jan 1, 2010) (*6) Appraisal by a licensed appraiser: Every 3 Year
4	Alternative Investments (excluding Real Estate)	Internal (in-house) Valuation: at least Every Year
5	Discretionary / Non-discretionary Fee-Paying / Non-fee-paying	See (*3) for the composite inclusion rules.
6	Allocation of Cash to Carve-Out Asset Class	Separate Accounts or Sub Accounts for each carve-out and hold the cash in each appropriate carve-out segment (*4)
7	After Acquisition	Non-compliant firm's results be brought into compliance within 1 year (*5)

(*1) Realized and/or Unrealized returns

(*2) GIPS states disclosure of calculation methodology changes are recommended, not required. However, the fact that material changes are not being disclosed is something completely different. Material changes would have to be disclosed. Failing to do so is a violation of the standards of professional conduct and GIPS. (e.g., Standard I(C) Misrepresentation)
Covered persons have an ethical obligation not to misstate facts or present information in a way that might mislead investors. Investment professionals violate the Standard when they know, or should know, that the presentation was biased or misleading. By violating the Standards in relation to GIPS, GIPS are also violated.

(*3)

Composite Inclusion Rules

		Fee-Paying	Non-Fee-Paying
	Discretionary	Yes	Yes
	Non-Discretionary	No	No

(*4) Allocation of cash to carve-out asset class is no longer sufficient starting on Jan 1, 2010. If an investment firm wants to report carve-out performance, the firm must set up separate accounts or sub accounts for each carve-out and hold the cash in each appropriate carve-out segment.

(*5) The Track record from a prior firm or a affiliation must be linked to or used to identify the record of a new or acquiring firm on a composite basis if (1) the new or acquiring firm employs substantially all of the prior firm or affiliation's investment decision makers (2) the decision making process has remained intact at the new or acquiring firm, and (3) appropriate records exist to support reported performance combinations of a compliant and a non-compliant firm require that the non-compliant firm's results be brought into compliance within 1 year.

(*6) GIPS Recommendation (not Requirement)
Valuation by an External Valuation Expert or Appraiser: at least Every Year

Trust

Definition:

• Trust is a legal relationship, not a person, under Common Law (e.g., US, UK).

Related parties:

• Settlor (or Grantor)  --(transfer assets)-->  Trustee
• Beneficiaries (e.g., settlor's children)

Discretionary Trust and Fixed Trust

Trust				Control of Distributions by
Discretionary				Trustee
Fixed				Predetermined terms (*1)

(*1) distributions thru (1) language in the trust document and/or (2) a non-binding letter of wishes

Irrevocable Trust and Revocable Trust

Trust			Beneficial Owner of Trust Assets	Legal Owner of Trust Assets (*2)
Irrevocable			Beneficiaries	Trustee (*3)
Revocable			Beneficiaries	Settlor

(*2) including Tax Payment due
(*3) In general, creditors (of a Beneficiary) are unable to reach assets that an individual (i.e., Beneficiary) does not own. (Just as an irrevocable trust can protect assets from claims against the Settlor, discretionary trust can protect assets from claims against the Beneficiaries.)

After-tax Return, Effective Long-Term Capital Gains Tax Rate, Future Value of the Portfolio, and Accrual Equivalent Return

Investment Portfolio = V₀ = $750,000
Average Annual Portfolio Pre-tax Return = r = 8.0%
Investment Time Horizon = n = 5 (years)
Cost Basis as a % of current market value = 100% = 1

Portfolio Expected Return Distribution

Source	First Year	Annual Proportion (p)		Tax Rate (t)
Tax Interest	$ 18,000	30.00 %		25 %
Dividends	$ 5,000	8.33 %		15 %
Short-Term Capital Gains	$12,000	20.00 %		25 %
Long-Term Capital Gains	$ 25,000	41.67 %		20 %
Total	$ 60,000	100.00 %

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[1] After-tax Return

r^* = r (1 - p_i t_i - p_d t_d - p_sg t_sg)

r^* = 8.00% * (1 - 0.3000 * 25% - 0.0833 * 15% - 0.2000 * 25%) = 6.90%


[2] Effective Long-Term Capital Gains Tax Rate

r^* T^* = r (p_lg t_lg)T^* = (r/r^*) (p_lg t_lg)

T^* = (8.00%/6.90%) * (41.67% * 20%)
= 9.66260869565217% = 9.66%

Also,
(r/r^*) = 1/(1 - p_i t_i - p_d t_d - p_sg t_sg)
# from the result of [1]
T^* = (p_lg t_lg)/(1 - p_i t_i - p_d t_d - p_sg t_sg)


[3] Future Value of the Portfolio

V_n = V₀ [1 + {(1 + r^*)ⁿ - 1} (1 - T^*)  -  (1 - B) t_lc]
= V₀ [{(1 + r^*)ⁿ (1 - T^*) + T^*}  -  (1 - B) t_lc]

V_n = $750,000 [{(1 + 6.90%)⁵ (1 - 9.66%) + 9.66%}  -  (1 - 1) 20%]
= 750000 * (((1 + 6.90%)^5 ^* (1 - 9.66%) + 9.66%)  -  (1 - 1) * 20%)
= 1,018,316.56847811 = 1,018,316.57


[4] Accrual Equivalent Return

V₀ (1 + R_AE)ⁿ = V_n
R_AE = (V_n/V₀)^1/n - 1

R_AE = (1,018,316.57 / 750,000)^1/5 - 1
= (1018316.57 / 750000)^0.20 - 1
= 0.0630759897687938 = 6.31%

Implementation Shortfall