Homework SourseIn the example the standard deviation of the portfolios retu
In the example, the standard deviation of the portfolio\'s return is lower than that of these two funds B and S. What is the intuition behind this? Is it always the case? Examine how the returns on these two funds behave. Do they move together or in opposite directions?
| portfolio proportions | |||||||||
| Bond | Stock | Bond | Stock | SD | Mean | ||||
| mean | 8.80% | 12.50% | 0 | 1 | 17.50% | 12.50% | |||
| VAR | 0.007536 | 0.030625 | 0.1 | 0.9 | 15.39% | 12.13% | |||
| SD | 8.68% | 17.50% | 0.2 | 0.8 | 13.34% | 11.76% | |||
| COV | -0.0066 | 0.3 | 0.7 | 11.36% | 11.39% | ||||
| Cor | -0.4345 | 0.4 | 0.6 | 9.52% | 11.02% | ||||
| 0.5 | 0.5 | 7.90% | 10.65% | ||||||
| 0.6 | 0.4 | 6.67% | 10.28% | ||||||
| 0.7 | 0.3 | 6.06% | 9.91% | ||||||
| 0.8 | 0.2 | 6.27% | 9.54% | ||||||
| 0.9 | 0.1 | 7.23% | 9.17% | ||||||
| 1 | 0 | 8.68% | 8.80% | ||||||
| | |||||||||
Solution
The intuition ia that the volatility reduces when assets with less than perfect correlation are combined because thia diveraifies the risk and hence standard deviation reduces. Only If correlation is less than +1, standard deviation of portfolio is always less than sum of individual standard deviation. This is not always the case but only when correlation is less than +1. The returns move in opposite directions.
