Portfolio Mgmt

Question 0

Variance of equally weighted portfolio

Answer 0

= (1/n)(avg variance) + [(n-1)/n](avg covariance)

Question 1

Covariance

Answer 1

= ρ(σ1)(σ2)

Question 2

Capital allocation line

Answer 2

• Line tangent to the efficient frontier
• Slope of the CAL represents best possible risk-return trade-off given the investor’s expectations

= Rf + [E(RT) - Rf]*(σC/σT)

Question 3

Capital market line

Answer 3

• CAL, assuming all investors have the same expectations
• New efficient frontier replacing Markowitz frontier to determine asset allocation to risk-free asset and market portfolio

= Rf + [(E(RM) - Rf)/όM]*όA

Question 4

Security market line

Answer 4

• shows relationship between an asset’s expected return and its systematic risk

= Rf + β[E(Rm - Rf)]

Question 5

β

Answer 5

Measure of asset’s systematic risk

= Cov/σm^2

= (ρ*σi)/σm

Question 6

Value added

Answer 6

= α - λ*ω^2

= residual return - (risk aversion x residual risk^2)

Question 7

Arbitrage portfolio

Answer 7

Factor sensitivities of zero to all factors, positive expected net cash flow, and an initial investment of zero

Question 8

Tracking portfolio

Answer 8

Specific set of factor sensitivities designed to replicate the factor exposures of a benchmark index

Question 9

Factor portfolio

Answer 9

Factor sensitivity of one to a particular factor in a multi-factor model and zero to all other factors

Question 10

Determining if an asset should be added to a portfolio

Answer 10

Only if the Sharpe ratio of the new asset is greater than the Sharpe ratio of the portfolio

E(Rnew) - Rf]/σnew > [[E(Rp) - Rf]/σp]*ρ(new,p)

Question 11

Information ratio

Answer 11

Measure of manager’s opportunities

= information coefficient x SQRT(breadth)

= ann. residual return/ann. residual risk

= t-stat/SQRT(years) for ex-post IR

Question 12

Information coefficient

Answer 12

Correlation between each forecast with the actual outcome (measure of skill)

= IC x SQRT[2/(1+r)]

Question 13

Total risk

Answer 13

Represented by σ

= systematic risk + unsystematic risk

Question 14

Systematic risk

Answer 14

Represented by β

Question 15

Adjusted β

Answer 15

= 0.333 + 0.667*β

Question 16

Arbitrage pricing theory - assumptions

Answer 16

• factor model describes asset returns
• investors can form well-diversified portfolios with many assets to eliminate asset-specific risk
• no arbitrage opportunities among well-diversified portfolios

Question 17

Optimal value added

Answer 17

= (IR^2)/(4risk aversion) = (IR^2)/(4λ)

= (ω*IR)/2

Question 18

Optimal residual risk

Answer 18

=IR/(2λ)

Question 19

Active risk

Answer 19

Based on active factor tilt and asset selection

(active risk)^2 = active factor risk + active specific risk