assigment 2
Marked Problem Set 2
Dagoberto Gonzalez Paez Student ID --65824138
November 28, 2013
1. Suppose that you can trade a riskless asset that yields 5% and two risky assets A and
B. The expected return of asset A is 8% and that of asset B is 11%, while the standard deviation of asset A is 14% and that of asset B is 23%. The covariance between assets
A and B is ?0:0322.
Solution . rA,B= CovAR(A,B) / [(σA)(σB)] = -0.0322 / (14%)(23%) rA,B = -1
But when rA,B = -1, (σp)^2 = [wA(σA) – wB(σB)]^2, σp = wA(σA) – wB(σB)
Is there is no risk fo the portafolio, then σp = 0
So this means that:
0 = 14%(wA) – 23%(1 – wA), solve this for wA, wA = 0.6216 wB = 1 – wA, wB = 0.3784
E(Rp) = 0.6216(8%) + 0.3784(11%) = 9.1352%
Suppose that each one of the securities has a value of $100,
Cash Flow Today
Cash Flow 1 year from today
Buy 0.6216 units of A
-$62.16
$62.16(1.08) = +$67.13
Buy 0.3784 units of B
-$37.84
$37.84(1.11) = +$42.00
Short 1 unit of risk-free
+$100
-$100(1.05) = -$105 Net Cash Flow
0
+$4.13
What today will be $4.13/(1.05) = $3.93
2. You are the risk manager in a major investment bank. The bank's current portfolio consists of U.S. stocks (50%), bonds (20%), and derivatives (30%). The expected returns and standard deviations of these investments are
Expected Return 13% 7% 25%
Standard Deviation 25% 9% 50%
A trader comes with a idea about investing in some new emerging markets: the markets of Polynesia, Micronesia, and New Caledonia. These markets have the following characteristics: Polynesia Micronesia New Caledonia
Expected Return 18% 20% 22%
Standard Deviation 30% 35% 28%
Correlation with Stocks 0.4 0.2 0.6
Correlation with Bonds 0.3 0.1 0.2
Correlation with Derivatives 0.2 0.3 0.4
Your job as risk manager is to determine how this investment would project the overall risk of the bank's portfolio. Based on risk considerations alone, which of the three
Dagoberto Gonzalez Paez Student ID --65824138
November 28, 2013
1. Suppose that you can trade a riskless asset that yields 5% and two risky assets A and
B. The expected return of asset A is 8% and that of asset B is 11%, while the standard deviation of asset A is 14% and that of asset B is 23%. The covariance between assets
A and B is ?0:0322.
Solution . rA,B= CovAR(A,B) / [(σA)(σB)] = -0.0322 / (14%)(23%) rA,B = -1
But when rA,B = -1, (σp)^2 = [wA(σA) – wB(σB)]^2, σp = wA(σA) – wB(σB)
Is there is no risk fo the portafolio, then σp = 0
So this means that:
0 = 14%(wA) – 23%(1 – wA), solve this for wA, wA = 0.6216 wB = 1 – wA, wB = 0.3784
E(Rp) = 0.6216(8%) + 0.3784(11%) = 9.1352%
Suppose that each one of the securities has a value of $100,
Cash Flow Today
Cash Flow 1 year from today
Buy 0.6216 units of A
-$62.16
$62.16(1.08) = +$67.13
Buy 0.3784 units of B
-$37.84
$37.84(1.11) = +$42.00
Short 1 unit of risk-free
+$100
-$100(1.05) = -$105 Net Cash Flow
0
+$4.13
What today will be $4.13/(1.05) = $3.93
2. You are the risk manager in a major investment bank. The bank's current portfolio consists of U.S. stocks (50%), bonds (20%), and derivatives (30%). The expected returns and standard deviations of these investments are
Expected Return 13% 7% 25%
Standard Deviation 25% 9% 50%
A trader comes with a idea about investing in some new emerging markets: the markets of Polynesia, Micronesia, and New Caledonia. These markets have the following characteristics: Polynesia Micronesia New Caledonia
Expected Return 18% 20% 22%
Standard Deviation 30% 35% 28%
Correlation with Stocks 0.4 0.2 0.6
Correlation with Bonds 0.3 0.1 0.2
Correlation with Derivatives 0.2 0.3 0.4
Your job as risk manager is to determine how this investment would project the overall risk of the bank's portfolio. Based on risk considerations alone, which of the three