| Tag | Value |
|---|---|
| file | Probability_uva-rules-for-expected-values-655-en_uva-rules-for-expected-values-655-en |
| name | uva-rules-for-expected-values-655-en |
| section | Probability/Elementary Probability/Random variables/Rules for expected values |
| type | num |
| solution | 12.65 |
| tolerance | 0 |
| Type | Calculation |
| Language | English |
| Level | Statistical Literacy |
Carla invests 30% of her funds in government bonds and 70% in a fund of common stocks. The return on an investment over a given period is the percentage change in price during that period. If X is the annual return of the government bonds and Y is the annual return of the stocks, then the return of the entire stock portfolio is R = 0.3X + 0.7Y. From a data set (dataset) of the yield in her equity portfolio over the period from 1995 to 2010, you see below data on the expectation values, the standard deviations, and on the correlations between X and Y. Based on this data, we have:
|X= annual government bond yield|μ X = 4.5%|σ X = 3.9%| |-|-|-| |Y = annual return on equity|μ X = 14.2%|σ X = 18.2% |-|-|. Correlation between X and Y || -0.12|
What is the standard deviation of return (σ R ) of investments distributed as a percentage? Round to two decimal places.
The correct answer is 12.65%.