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Homework answers / question archive / You are given the following information on the future states of the economy and returns for 2 risky securities i and j
You are given the following information on the future states of the economy and returns for 2 risky securities i and j. Assume that the Risk-Free rate of interest is 2.0% per year. Scenario Probability Very Good 25.00% Return for Security Return for Security i j -20.00% 5.00% 10.00% 20.00% 30.00% -12.00% Good 25.00% 25.00% Average Poor 25.00% 50.00% 9.00% Compute the following items:
Draw a Graph as follows: You may Use any Software
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E[Rp] on the Y- Axis : Range 0% to 15% in increments of 1% (clearly marked on the Y- Axis).
Sigma p on the X-Axis: Range 0% to 20% in increments of 1% (Clearly Marked on the X - Axis)
Draw a hyperbola (curve for) weights in security i, j from (-0.3, 1.3) to (1,0) in increments of 0.10 (14 points).
Draw the Capital Allocation Line Marking all relevant points clearly.
| Scenario | Probability (p) | Return for Security i (A) | Return for Security j (B) | ( A * p ) | ( B * p ) | d (A)= A- ER(i) | d2 (A) * p | d (B) = B- ER(j) | d2 (B) * p |
| Very Good | 0.25 | -20% | 5% | - 5% | 1.25% | -20 - 17.5 = -37.5 | (-37.5)2 * 0.25 = 351.56 | 5 - 5.5 = -0.5 | (-0.5)2 * 0.25 = 0.06 |
| Good | 0.25 | 10% | 20% | 2.5% | 5% | 10 - 17.5 = -7.5 | (-7.5)2 * 0.25 = 14.06 | 20 - 5.5 = 14.5 | (14.5)2 * 0.25 = 52.56 |
| Average | 0.25 | 30% | -12% | 7.5% | - 3% | 30 - 17.5 = 12.5 | (12.5)2 * 0.25 = 39.06 | -12 - 5.5 = -17.5 | (-17.5)2 * 0.25 = 76.56 |
| Poor | 0.25 | 50% | 9% | 12.5% | 2.25% | 50 - 17.5 = 32.5 | (32.5)2 * 0.25 = 264.06 | 9 - 5.5 = 3.5 | (3.5)2 * 0.25 = 3.06 |
| Total ( ∑ ) | 1.00 | 17.5% | 5.5% | 668.74 | 132.24 |
Expected Return of Security i = [ ∑ (A*p) ] / ∑p = 17.5 / 1 = 17.5%
Expected Return of Security j = [ ∑ (B*p) ] / ∑p = 5.5 / 1 = 5.5%
Standard Deviation of Security i = √ [ d2 (A) * p ] / ∑ p = √ 668.74 = 25.86%
Standard Deviation of Security j = √ [ d2 (B) * p ] / ∑ p = √ 132.24 = 11.50%
| w1 (i) | w2 (j) | ER (p) = ER (i) * w1 + ER (j) * w2 | SD (p) = SD (i) * w1 + SD (j) * w2 | |
| -0.3 | 1.3 | 1.9 | 7.19 | |
| -0.2 | 1.2 | 3.1 | 8.63 | |
| -0.1 | 1.1 | 4.3 | 10.06 | |
| 0 | 1 | 5.5 | 11.50 | |
| 0.1 | 0.9 | 6.7 | 12.94 | |
| 0.2 | 0.8 | 7.9 | 14.37 | |
| 0.3 | 0.7 | 9.1 | 15.81 | |
| 0.4 | 0.6 | 10.3 | 17.24 | |
| 0.5 | 0.5 | 11.5 | 18.68 | |
| 0.6 | 0.4 | 12.7 | 20.12 | |
| 0.7 | 0.3 | 13.9 | 21.55 | |
| 0.8 | 0.2 | 15.1 | 22.99 | |
| 0.9 | 0.1 | 16.3 | 24.42 | |
| 1 | 0 | 17.5 | 25.86 |
Here we assume weights of risky asset and risk free asset. And for claculation we assume both security i , j have 50% - 50% allocation
Rp = portfolio return containing risky asset and risk free asset
Sd is Standard Deviation. Risk free rate is 2%
X axis shows standard deviation and Y axis shows Rp i.e., expected return.
please see the attached file for the complet solution.
