CFA III SS 8 Asset Allocation

• Dynamic: risk and return in one period affects performance in subsequent periods; difficult and costly; preferred for ALM
• Static: ignores correlation among periods

• loss aversion
• mental accounting
• fear of regret

• individual has shorter time horizon (usu) so can use additive
• for institutional or longer term horizons, multiply (1+infl)(1+spend)(1+mgmt fees)

• Note: variance, not standard deviation
• equation is for whole percentages
• if use decimals, including std dev in decimal form, change to 0.5
• A = investors risk aversion score from 1-10, 1-3 is low risk aversion, 7-10 is high

• semivariance
• target semivariance
• shortfall risk: risk of exceeding a maximum acceptable dollar loss
• semivariance: variance calculated using only returns below the expected return
• target semivariance: semivariance below some target minimum return (as opposed to expected return)

• Rmar = minimum acceptable return
• IF Rmar < Rf, use Rf

• 1. Assets are homogenous with high positive correlation
• 2. Asset classes are mutually exclusive
• 3. Asset classes are diversifying with low correlation
• 4. The classes include most of the world's investable assets
• 5. Asset classes are sufficiently liquid to allow investment

if  AND asset is permissible by the investor's constraints, then asset should be added

• Currency
• Home country bias
• Political
• Costs - less liquid; higher transaction costs; free float (market cap greater than investable shares); lack of information; infrastructure and facilities create high clearing and custody fees
• Contagion - correlations are higher in a crisis, when diversification is most needed; could use two correlation matrices, one for normal periods and one for crisis

• Pros: higher capital flow into market could drive up prices; beta becomes the risk rather than standalone risk, which is usually higher; volatility declines; lowers cost of capital, increasing prices and liquidity
• Cons: decreases diversification benefit

• 1. mean-variance optimization (MVO)
• 2. resampled efficient frontier
• 3. black-litterman
• 4. monte carlo simulation
• 5. asset-liability management
• 6. experienced-based 

• E(r), stnd dev, and correlation are estimated, then put into a model to optimize risk for each return level - aka efficient frontier
• Can be unconstrained (allow short sales) or constrained (only positive weights
• Constrained is more practical as unconstrained can lead to strange/unrealistic weights
• Cons: frontier is unstable - highly sensitive to inputs; maintaining weighting is costly

• like MVO, but inputs have associated probabilities and run through monte carlo
• efficient frontier is more like a blur
• optimal allocation for a single resampled portfolio is the average of possible allocations
• Pros: generates more stable asset allocations; addresses inability to know true input values
• Cons: no statistical rationale for the process; historical initial data may not be indicative of future values

• manager inputs global asset weights and covariances, and reverse optimizes for implied returns by asset class
• manager can adjust returns based on his outlook on the economy
• final results can be put into an MVO model, or start with the global portfolio and adjust weights based on views
• Pros: by starting with global portfolio, generally produces well diversified portfolios; reduces bias input as returns are anchored to current returns
• Cons: complex and uses historical values that may not reflect future performance

• Pros: overcomes the static nature of MVO; used for ALM analysis
• Cons: complex; expensive; dependent on quality of inputs

• uses MV analysis to optimize growth of surplus in relation to volatility of surplus
• surplus = present value assets (PVA) - PVL
• plot efficient frontier of surplus with far left point being Minimum Surplus Variance (MSV)
• vertical axis of efficient frontier graph is (PVA-PVL), horizontal is standard deviation
• Pros: considers allocation of assets with respect to liabilities; can assess probability of meeting liabilities
• Cons: estimation bias; must be incorporated with another approach (ex monte carlo) to address multi-period concerns

• Use heuristics, such as
• 1. Long time horizons increase ability to bear risk
• 2. Neutral allocation for the average investor is 60/40
• 3. Subtract investors age from 100 to determine preferred allocation to equities
• Pros: generally consistent with more sophisticated techniques; simple and cheap
• Cons: not based on sound investment theory; allocation rules may be too simple for some investors

• use small number of corner portfolios to approximate the efficient frontier
• only applies for sign constrained portfolios
• corners are when the weight of an asset go to or from 0 as move from left to right along efficient frontier
• linear combination between corners for desired return, and linear combination to determine final portfolio standard deviation

• Create capital allocation line (CAL) between Rf and portfolio with highest Sharpe ratio
• CAL dominates all other portfolios, other than the tangency portfolio
• Note must be able to short Rf to gain higher return than tangency portfolio

Deviate from the optimal allocation to take advantage of mispricings and add alpha