"quantity"exercise:Variance of portfolio

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Questions 1:

A stock’s expected price movement over the next two periods is as follows:

quantity exercise:Variance of portfolio

The initial value of the stock is $80. The probability of an up move in any given period is 75%, and the probability of a down move in any given period is 25%. Using the binomial model, the probability that the stock’s price will be $79.20 at the end of two periods is closest to:

A、 37.50%.

B 、56.25%.

C 、18.75%.

Questions 2:

An equally weighted portfolio is composed of four stocks. An analyst knows the mean and variance for each of the four stocks. In order to estimate the portfolio mean and variance, the analyst will require the stocks’:

A、 skewness.

B 、pairwise correlations.

C、 kurtosis.

View answer resolution

【Answer to question 1】A

【analysis】

A is correct. Across two periods, there are four possibilities:

quantity exercise:Variance of portfolio

■ uu: End Value: $96.80

■ ud: End Value: $79.20

■ du: End Value: $79.20

■ dd: End Value: $64.80

where u is an up move and d is a down move. The probability of an up move followed by a down move is 0.75 × 0.25 = 0.1875. The probability of a down move followed by an up move is 0.25 × 0.75 also = 0.1875. Both of these sequences result in an end value of $79.20. Therefore, the probability of an end value of $79.20 is (0.1875 + 0.1875) = 37.5%. Alternatively, the following formula could be used:

quantity exercise:Variance of portfolio

n = 2 (number of periods)

x = 1 (number of up moves: ud and du)

p = 0.75 (probability of an up move)

quantity exercise:Variance of portfolio

B is incorrect because it is the probability of an up move followed by an up move (0.75 × 0.75 = 0.5625).

C is incorrect because it is does not recognize that there are two branches that end in $79.20.

【Answer to question 2】B

【analysis】

B is correct. Specification of the mean and variance for a portfolio of four stocks requires estimates of the mean returns and variances for each of the four stocks and the pairwise correlations between each of the four stocks.

A is incorrect because skewness measures are not required to estimate the mean and variance of a portfolio.

C is incorrect because kurtosis measures are not required to estimate the mean and variance of a portfolio.

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