Returns on stocks X and Y are listed below:
Period | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
Stock X | 9% | 5% | 6% | -2% | 1% | -3% | 11% |
Stock Y | -4% | 3% | 10% | 7% | 5% | -3% | 2% |
Consider a portfolio of 40% stock X and 60% stock Y.
What is the (population) standard deviation of portfolio returns?
Please specify your answer in decimal terms and round your answer to the nearest thousandth (e.g., enter 12.3 percent as 0.123).
Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.
X | P(X) | Y | P(Y) | Z = X*P(X)+Y*P(Y) | (Z-mean)² | |||
0.09 | 0.4 | -0.04 | 0.6 | 0.012 | 0.00042 | |||
0.05 | 0.4 | 0.03 | 0.6 | 0.038 | 0.00003 | |||
0.06 | 0.4 | 0.1 | 0.6 | 0.084 | 0.00264 | |||
-0.02 | 0.4 | 0.07 | 0.6 | 0.034 | 0.00000 | |||
0.01 | 0.4 | 0.05 | 0.6 | 0.034 | 0.00000 | |||
-0.03 | 0.4 | -0.03 | 0.6 | -0.03 | 0.00392 | |||
0.11 | 0.4 | 0.02 | 0.6 | 0.056 | 0.00055 |
Z=X*P(X)+Y*P(Y) |
(Z-mean)² | ||
total sum = | 0.228 | 0.00757 |
mean = 0.228/7 = 0.033
variance = 0.00757/7 = 0.00108
std dev = √(variance) =
0.033
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