Suppose you are an investor with a choice between three securities that are iden
ID: 1097081 • Letter: S
Question
Suppose you are an investor with a choice between three securities that are identical in every way except in terms of their rates of return and risk. Which security has the least risk (smallest standard deviation)?
Investment A: total return = 10 percent with probability 50 percent
total return = 20 percent with probability 50 percent
Investment B: total return = 12 percent with probability 50 percent
total return = 18 percent with probability 50 percent
Investment C: total return = 5 percent with probability 60 percent
total return = 25 percent with probability 40 percent
Select one:
1. Investment A
2. Investment B
3. Investment C
4. Investments A and B have the same risk, which is less than that of investment C.
Explanation / Answer
Hi,
The correct answer is as follows
Expected return on stock A = 10%*50%+20%*50%
15%
Standard Deviation of stock A = sqroot((15%-10%)^2*50%+(15%-20%)^2*0.5)
=5%
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Expected Return on Stock B = 12%*50%+18%*50%
=15%
Std. Deviation of stock B = sqroot((15%-12%)^2*50%+(15%-18%)^2*0.5)
=3%
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Expected return on stock C= 5%*60%+25%*40%
=13%
Std. Deviation on stock C = sqroot((13%-5%)^2*60%+(13%-25%)^2*0.4)
=9.78%
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Since, the standard deviation of stock B is the lowest, it is the least risky stock
Hence, option (B), is the correct answer