2. Consider the following scenario analysis involving asset X and asset Y: Econo
ID: 2427521 • Letter: 2
Question
2. Consider the following scenario analysis involving asset X and asset Y:
Economic Condition
Probability
Return on X
Return on Y
Boom
0.1
30%
12%
Accelerated Growth
0.2
20%
10%
Normal Growth
0.4
15%
9%
Slowdown
0.2
10%
8%
Recession
0.1
-50%
-4%
Note: Careful with rounding!
a)Compute the expected returns and the standard deviations for both assets.
b)Compute the correlation coefficient between the returns on the two assets.
c)Can you build a portfolio of assets X and Y with zero risk? Prove that your portfolio is indeed riskless.
Economic Condition
Probability
Return on X
Return on Y
Boom
0.1
30%
12%
Accelerated Growth
0.2
20%
10%
Normal Growth
0.4
15%
9%
Slowdown
0.2
10%
8%
Recession
0.1
-50%
-4%
Explanation / Answer
3- no a zero risk portfolio can not be prepared with security X and Y because to built a zero risk portfolio equal investment in two securities with equal return and standard deviation. a constant portfolio return deviation Pij = -1 implies that return on one security is the mirror image of return of another security held in the portfolio. thus an equal investment in two securities with same rate of return and standard deviation but a perfect inverse correlation will have constant return value over time. this never changes into value. and with two securities X and Y zero risk portfolio cann not be preapred.
Economic Condition Probability Return on X Return on Y Probability Boom 0.1 30% 0.03 12% 0.1 0.012 Accelerated Growth 0.2 20% 0.04 10% 0.2 0.02 Normal Growth 0.4 15% 0.06 9% 0.4 0.036 Slowdown 0.2 10% 0.02 8% 0.2 0.016 Recession 0.1 -50% -0.05 -4% 0.1 -0.004 Return on security X 0.1 Return on Security Y 0.08 Standard deviation 0.041833 Standard deviation 0.014422 Answer No 2 Return of X Return of Y 0.03 0.012 0.04 0.02 0.06 0.036 0.02 0.016 -0.05 -0.004 Correlation between X and Y 0.928191Related Questions
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