Expected Return and Standard Deviation This problem will give you some practice calculating measures of prospective portfolio performance.

Question

Expected Return and Standard Deviation This problem will give you some practice calculating measures of prospective portfolio performance.
There are two assets and three states of the economy:

Rate of Return if State Occurs
Stock B	Stock A	Probability of State of Economy	State of Economy
.20	-.15	.20	Recession
.30	.20	.50	Normal
.40	.60	.30	Boom

What are the expected returns and standard deviations for these two stocks?

Accepted Answer

The expected returns are just the possible returns multiplied by the associated probabilities:

[latex]E(R_{A})[/latex]=(.20×-.15)+(.50×.20)+(.30×.60)=25%

[latex]E(R_{B})[/latex]=(.20×.20)+(.50×.30)+(.30×.40)=31%

The variances are given by the sums of the squared deviations from the expected returns multiplied by their probabilities:

[latex]σ^{2}_{A}=.20×(-.15-.25)^{2}+.50×(.20-.25)^{2}+.30×(.60-.25)^{2}[/latex]

=[latex](.20×–.40^{2})+(.50×–.05^{2})+(.30×.35^{2})[/latex]

=(.20×.16)+(.50×.0025)+(.30×.1225)

=.0700

[latex]σ^{2}_{B}=.20×(.20-.31)^{2}+.50×(.30-.31)^{2}+.30×(.40-.31)^{2}[/latex]

=[latex](.20×-.11^{2})+(.50×-.01^{2})+(.30×.09^{2})[/latex]

=(.20×.0121)+(.50×.0001)+(.30×.0081)

=.0049

The standard deviations are thus:

[latex]σ_{A}=\sqrt{.0700}[/latex]=26.46%

[latex]σ_{B}=\sqrt{.0049}[/latex]=7%

Question 13.S-T.1: Expected Return and Standard Deviation This problem will giv...

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