Asset Allocation

Question 1

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Asset Allocation Approaches: Investment Objective

Answer 1

1. Asset Only:

• Use MVO,
• max port’s sharpe,
• diversification, correlations with other assets you hold and liquidity are also relevant

2. Liability Relative:

• duration, inflation and credit-risk should be closely monitored.
• Fund status impacts the risk profile b/w liability-hedging and return seeking (why increase risk if you are overfunded?).

3. Goal-based asset allocation:

• built into behavioral finance (mental accounting bias).
• Adds riskier assets that are accepted by the investor due to its context in the portfolio

Question 2

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Super asset classes

as defined by Greer (1997)

Answer 2

1. Capital Assets - generates dividends, CF or interest - value determined by NPV (eg. stocks, bonds, etc)

2. Consumable/transformable assets - commodities that are transformed into something else (eg. petroleum)

3. Store of value assets - no income or economic value (eg. art, currencies, precious metals except in industrial application)

Question 3

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Criteria for specifying an Asset Class

Greer (1997)

Answer 3

1. Homogeneous - similar attributes

2. Mutually Exclusive - Overlapping is a problem (eg. Emerging mkt are a diff class)

3. Diversifying - ρ w/ other class > 0.95 = undesirable.

4. Must be representable

5. Capacity for allocation / Liquidity

Question 4

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Expected Utility (MVO)

Answer 4

U_m = E(R_m) − 0.005 * λ * σ²_m
Certainty-equivalent return (comparable to the risk-free**)

where

λ = the investor’s risk aversion coefficient - investor’s risk-return trade-off (how much inv will forgo return for lowering risk). 0 = risk neutral 4 = risk moderate

DEIXAR O RESTANTE EM % MESMO > 14%² = 196

Question 5

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SFRatio vs Sortino Ratio

Answer 5

RSF = (R_P – M_inimumA_cceptableR_eturn) / σ_P

Sortino = (R_P – M_inimumA_cceptableR_eturn) / Downside Deviation

Question 6

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SFRatio

Answer 6

RSF = (R_P – M_inimumA_cceptableR_eturn) / σ_P

Question 7

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Criticisms of MVO

Answer 7

1. Highly concentrated / Too sensitive (large shifts w/ small changes)
2. Assumes a normal distribution of returns.
3. Diversification by asset class ≠ diversification by risk source
4. Single-period model = ignores taxes, transaction costs, inflation or liabilities.

Question 8

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Criticisms of MVO

X Highly concentrated / Too sensitive (large shifts w/ small changes)

Answer 8

• Reverse optimization - less dependent on estimates of return.
  
  • Start with ρ, σ, and benchmark weights (or another optimal target).
  • Then use MVO to solve for expected return by asset class.
• Black-Litterman - less dependent on estimates of return and tends to include more classes
  
  • Reverse optimization + Manager views to adjust MVO
• Monte Carlo (Resampling) - deals directly with the uncertainty of estimating returns.
  
  • It starts with MVO and the manager’s best estimates of return and other inputs.
  • Then the return data is varied up and down (Monte Carlo). The avg EF of each allocation is selected.

Question 9

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Criticisms of MVO

Diversification by asset class ≠ diversification by risk source

Answer 9

• Factor-based allocation (i.e. mkt risk premium, mkt cap, value vs. growth, mkt momentum vs. mean reversion, duration, etc)

Question 10

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Criticisms of MVO

Assumes a normal distribution of returns.

Answer 10

Non-normal optimization

Question 11

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Criticisms of MVO

Single-period model

Answer 11

1. Goals based approach – suited to individuals w/ multiple goals (sub-portfolios)
2. Liability-relative Asset Allocation – model liabilities as part of MVO and use Monte Carlo on how portfolio performs over time

• Surplus optimization: surplus efficient frontier (min Vol & max Er)
• “two-portfolio”: Hedging / Return seeking portfolio (for the surplus)
• Asset-liability approach (ALM): simultaneously alter charact. of assets and liabilities. Multi-period, more complex.

Question 12

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• *Risk Budgeting**
• “use risk efficiently in the* persuit of return”

Marginal Contribution to Risk (MCTR)

Absolute Contribution Total Risk (ACTR)

% Contribution to Total Risk

Ratio of Excess Return to MCTR

Answer 12

• *MCTR =** β_Asset x σ_Portfolio
• Excess Return to MCTR = (Er - Rf) / MCTR*
• *ACTR =** Weight_Asset x MCTR
• total sum is equal to the portfolio’s risk*

% Contribution to Total Risk = ACTR / Portfolio σ

Question 13

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Optimal corridor size

Answer 13

(+) related to the optimal corridor size:

Risk Tolerance

Correlation of asset classes

Transaction Costs

(-) related to the optimal corridor size:

Volatile asset class

Volatile portfolio

Question 14

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Heuristic asset allocation

5 strategies that simplify allocation

Answer 14

1. 120 - age (exposure to equity)
2. 60/40 stock/bond
3. Endowment Model - large allocation to non-traditonal assets
4. Risk Parity - distributes equally the risk b/w assets in a port
5. The 1/N rule - equally weighted asset allocation (regret aversion)

Question 15

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Behavioral Biases in Asset Allocation

Answer 15

FILMAR

1. Framing
2. Illusion of Control
3. Loss Aversion
4. Mental Accounting
5. Availability
6. Representativeness

Question 16

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FX - Return & volatility

Answer 16

R_DC = (1 + R_FC) * (1 + R_FX) -1

_{<span>σ²</span>}(R_DC) ≈ _{<span>σ²</span>}(R_FC) + _{<span>σ²</span>}(R_FX) + 2 * _{<span>σ</span>}(R_FC) * (R_FX) * ρ(R_FX,R_FX)

REMEMBER: _{<span>σ² = Variance; σ = STD Dev = Volatility</span>}

Question 17

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Hedge ratio

Answer 17

Hedge ratio = ρ * σ_DC / σ_FX

Question 18

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Using Sharpe to check if an Asset improves mean-variance

Answer 18

Sharpe_Asset > Sharpe_Portfolio * ρ

Question 19

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Hedging Multiple FX

Answer 19

Mostly used when one asset (FX) is held long and the other short. If you have 2 FX with high correl, but both long, you will have to hedge both positions

1. Cross hedges – one currency is used to hedge another that is similar, but not exact (correlations may change and expose port)
2. Macro hedges – hedge portfolio-wide risk instead of single currency risk. Short a basket of currencies (derivative). Less expensive
3. A minimum variance hedge ratio (MVHR) - regression-based approach = cross hedge + macro hedge. H = [σ_(InvestorFX) / σ_(ExposureFX)] * ρ

• Texas Hedge – Opposite of hedge, doubles the exposure

Question 20

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FX Hedge Strategies

Answer 20

1. Passive: Match FX exposure of benchmark
2. Discretionary: risk reduction with deviations from the benchmark to add value.
3. Active: Allow wider deviations.
4. Overlay: separate manager for FX management. Treat currency as an asset class (pure value-added approach).

Question 21

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Shrinkage estimator

Answer 21

Shrinkage estimation = weighted avg of a parameter + weighted parameter reflecting analyst’s relative belief

Question 22

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Hedging emerging market currencies challenges

Answer 22

challenges:

(1) larger bid-asked spreads that expand during crises,
(2) returns negative skew and fat tails,
(3) correlations rise during crisis,
(4) tail risk as governments support FX with severe currency value correction after,
(5) restrict flow - solution = NDF (net settlement in the developed country FX)