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%