The standard deviations of the returns as %ages are shown below: S&P 500 =1.47 H

Question

The standard deviations of the returns as %ages are shown below:
S&P 500 =1.47
Hewlett Packard (HPQ) =2.55
AT&T(T)=1.15
CiscoSystems (CSCO)=2.22

If we construct a portfolio of the 2 tech stocks, Hewlett Packard and Cisco
the standard deviation as a %age is shown below:

Portfolio: Hewlett Packard + Cisco =2.03%

Explain why the value lower is lower than either of the two stocks alone.

If the relevant annual risk free rate is 3% and the market risk premium is 2.5%,
calculate the expected annual rates of return (%) for Hewlett Packard, AT&T and
Cisco.

Explanation / Answer

The value is lower than the stocks alone , because of co-variance or correlation present in the stocks which must be negative to support the above fact.

_portfolio^2 =(w1*_HPQ) ^2 + (w2*_Cisco)^2 + 2 * w1*w2*covariance(HPQ,Cisco)

Expected returns

HPQ = Rf + RiskMkt/Risk_HP*(Mkt risk premium) = 3% + 2.5 %*(1.47/2.55) = 4.441%

CSCO = 3% + 2.5% * 1.47/2.22 = 4.655%

AT&T = 3% + 2.5% * 1.47/1.15 = 6.1956%

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