Calculation Section

Average return and risk

The table below is going to show the average return and the standard deviation (StD) of the two stocks – California R.E.I.T. and Brown Group, Inc in two years 1989 and 1990.

Stock | Cal. REIT | Brown | SP500 |

AVERAGE | -2.27% | -0.67% | 1.10% |

STDEV | 9.23% | 8.17% | 4.61% |

The figures were calculated using Excel’s STDEV and AVERAGE function with the provided return of two companies, California R.E.I.T. and Brown Group, Inc as well as S&P 500 index. Regarding to the result, both Stocks are more volatile than SP500 because of its standard deviation which was almost double the size of SP500 even SP500 index had the highest average return. By saying that, California R.E.I.T. and Brown Group, Inc are expected to have a higher return than the market index in the following year to trade off the risk. Also, California REIT seems to be riskier than Brown Inc caused by higher standard deviation. This is expected, as explained above, since these two companies belong to two completely different industries and during 1990s period real estate investment trust industry was experiencing a considerably recession stage. That could be explain why the Cal. REIT stock appears to be riskier.

Assets allocation and portfolio evaluation

To calculate the standard deviation of a portfolio with 2 assets, namely asset A and asset B, the formula used is below:

σp= [ωA2σA2 + ωB2σB2 + 2ωAωBσAσBρAB]1/2

In this formula, σA and σB are Standard Deviation of asset A and asset B, and ρAB is the covariance between asset A and B. Using Excel’s COVAR function, we can calculate the covariance between Vanguard 500 Index and the two stocks.

Stock | Cal. REIT | Brown Group |

Covariance (Vanguard, Stock) | 0.0003 | 0.0024 |

The StD of the portfolio SPC with 99% invested in S&P index fund and 1% in Cal. REIT is:

= [(0.99)2(0.0461)2 + 2(0.99) (0.01) (0.0003) + (0.01)2(0.0923)2]1/2 = 4.57%

The StD of the portfolio SPB with 99% invested in S&P index...