2.5 Measures of Risk and Performance

Question 1

Semi-variance

Answer 1

• average squared deviations below the mean

(Σ of all Rt below the mean [Rt - E(R)]^2) / T - 1

Question 2

Semi-standard Deviation

Answer 2

• sq. root of the semi-variance

Question 3

Tracking Error

Answer 3

• extent to which investment returns deviate from the benchmark returns over time

√ (Σ ((Rt - Rb) - M)^2 / T - 1)

Where Rb is benchmark return, M is mean difference between investment return and benchmark return

Question 4

Parametric VaR

Answer 4

= z * σ* √days * value

z = critical value for one-tailed test
σ = std dev of daily returns
√days = sq root of the number of days specified
Value = value of investment portfolio

Question 5

Z-values

Answer 5

90% VaR: use z-value of 1.28
95% VaR: use z-value of 1.65
99% VaR: use z-value of 2.33

Question 6

VaR Calculation

Answer 6

• measure of potential loss ie: worst possible loss under normal conditions, over a specified period, for a given confidence level

Question 7

Aggregating VaR - perfect positive correlation

Answer 7

VaRp = VaR1 + VaR2

Question 8

Aggregating VaR - perfect negative correlation

Answer 8

VaRp = VaR1 - VaR2

*cancel each other out with diversification

Question 9

Aggregating VaR - zero correlation

Answer 9

VaRp = √VaR1^2 + VaR2^2

Question 10

Sharpe Ratio

Answer 10

• expected return (in excess of the risk free rate) per unit of total risk (σ)

(E(Rp) - Rf) / σp

• use for total portfolio, not components

Question 11

Monthly Sharpe Ratio

Answer 11

[(E(Rp) - Rf) / 12] / σp/√12

Question 12

Treynor Ratio

Answer 12

• expected excess return earned per unit of systematic risk

TR = (E(Rp) - Rf) / βp

Question 13

Sortino Ratio

Answer 13

• expected excess return for a portfolio over a target return divided by target semi standard deviation

= (E(Rp) - Rt) / TSSD

Question 14

Information Ratio

Answer 14

IRp = (E(Rp) - Rbenchmark) / Tracking Error of portfolio

Question 15

Return on VaR

Answer 15

RoVaR = E(Rp) / VaR

Question 16

Jensen’s Alpha

Answer 16

aka alpha

α = Rp - [Rf + βp(Rm - Rf)]

Question 17

M2 Approach

Answer 17

• risk adjusted measure of portfolio return
• expected return on a leveraged portfolio that has same standard deviation as the market index

M2 = Rf + (σm/σp)[E(Rp) - Rf]