# Risk and Return: Past and Prologue

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Risk and Return: Past and Prologue
CHAPTER 05
RISK AND RETURN: PAST AND PROLOGUE

1. The 1% VaR will be less than –30%. As percentile or probability of a return declines so does the magnitude of that return. Thus, a 1 percentile probability will produce a smaller VaR than a 5 percentile probability.

2. The geometric return represents a compounding growth number and will artificially inflate the annual performance of the portfolio.

3. No. Since all items are presented in nominal figures, the input should also use nominal data.

4. Decrease. Typically, standard deviation exceeds return. Thus, an underestimation of 4% in each will artificially decrease the return per unit of risk. To return to the proper risk return relationship the portfolio will need to decrease the amount of risk free investments.

5. Using Equation 5.6, we can calculate the mean of the HPR as:
E(r) = = (0.3  0.44) + (0.4  0.14) + [0.3  (–0.16)] = 0.14 or 14%
Using Equation 5.7, we can calculate the variance as:
Var(r) = 2 = – E(r)]2
= [0.3  (0.44 – 0.14)2] + [0.4  (0.14 – 0.14)2] + [0.3  (–0.16 – 0.14)2]
= 0.054 Taking the square root of the variance, we get SD(r) =  = = = 0.2324 or 23.24%

6. We use the below equation to calculate the holding period return of each scenario:
HPR =
a. The holding period returns for the three scenarios are: Boom: (50 – 40 + 2)/40 = 0.30 = 30% Normal: (43 – 40 + 1)/40 = 0.10 = 10% Recession: (34 – 40 + 0.50)/40 = –0.1375 = –13.75%

E(HPR) =
= [(1/3)  0.30] + [(1/3)  0.10] + [(1/3)  (–0.1375)]
= 0.0875 or 8.75% Var(HPR) = – E(r)]2
= [(1/3)  (0.30 – 0.0875)2] + [(1/3)  (0.10 – 0.0875)2]
+ [(1/3) (–0.1375 – 0.0875)2] = 0.031979 SD(r) =  = = = 0.1788 or 17.88%

b. E(r) = (0.5  8.75%) + (0.5  4%) = 6.375%  = 0.5  17.88% = 8.94%

7.
a. Time-weighted average returns are based on year-by-year rates of return.

Year Return = [(Capital gains + Dividend)/Price]
2010-2011