Question

1. Which one of the following is the best interpretation of this VaR statistic: Prob (R_p ≤ - 0.15) = 37%?

• Your portfolio is expected to lose at least 15 percent, but not more than 37 percent in any given year.

• Sometime in the future, your portfolio is expected to lose 15 percent or more in a single year, but have an overall average rate of return of 37 percent.

• There is a 37 percent chance that your portfolio will decline in value by at least 15 percent over the next year.

• If your portfolio declines by 15 percent or more, that decline is expected to be followed by a 37 percent increase in value.

• There is a 37 percent chance that your portfolio will lose at least 15 percent of its value over the next 10 years.
  
  
  2.

  What is the Treynor ratio of a portfolio comprised of 40 percent portfolio A, 25 percent portfolio B, and 35 percent portfolio C?

  Asset	Weight		Avg Return		Std Dev		Beta
  A	40	%	15.30	%	17.20	%	1.56
  B	25	%	10.50	%	9.80	%	0.95
  C	35	%	13.30	%	14.10	%	1.25

  The risk-free rate is 2.9 percent and the market risk premium is 8.6 percent.

  Multiple Choice

• 0.054

• 0.062

• 0.081

• 0.070

• 0.102

Answer 1

1]

Value at Risk gives the probability of losing more than a given amount on a given portfolio over a period of time.

In this question, the best interpretation is :

There is a 37 percent chance that your portfolio will decline in value by at least 15 percent over the next year.

R_{p =} probability of decline

VaR = 37% - this is the quantity of loss for the given probability

VaR is usually measure for years, months, days. etc. It is rarely measured for a 10-year period. Hence the last interpretation is unlikely to be the best interpretation.

2]

Treynor ratio = (portfolio return - risk free rate) / portfolio beta

portfolio return = weighted average return of each asset

portfolio return = (40% * 15.3%) + (25% * 10.5%) + (35% * 13.3%) ==> 13.4%

portfolio beta = weighted average beta of each asset

portfolio beta = (40% * 1.56) + (25% * 0.95) + (35% * 1.25)

portfolio beta = 1.30

Treynor ratio = (13.4% - 2.9%) / 1.30

Treynor ratio = 0.081