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Suppose your client is risk-averse but can invest in only one of the three secur

ID: 3250650 • Letter: S

Question

Suppose your client is risk-averse but can invest in only one of the three
securities, A, B, or C, in an uncertain world characterized as follows. Next year
the economy will be in an expansion, normal, or recession state with
probabilities 0.30, 0.43, and 0.27, respectively. The returns (%) on the securitiies
in these states are as follows: Security A {expansion = +15.24, normal = +9.50,
recession = +7.00}; Security B {+10.00, +7.50, +5.00}; Security C {+13.50, +11.00,
+6.50}. Which security can you rule out, that is, you will not advise your client to
invest in it?

Explanation / Answer

The situation would be clear if we make a contingency table showing this information:

In the above table, we can see that for security B,the return is less than both A and C in any economic scenario.

Hence,

We can rule out security B.

Security Expansion Normal Recession A +15.24 +9.50 +7.00 B +10.00 +7.50 +5.00 C +13.50 +11.00 +6.50
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