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Chrome File Edit View History Bookmarks People Window Help Grades for Ahmad D anhi × y D Week 5 Chapters x G Refer To Table 12- x e Search Textbook S x , G math calculator Cx × (-? ? ezto.mheducation.com/hm.tpx a t Consider the following information about three stocks Rate of Return If State Occurs State of Economy Probability of State of Economy 0.25 0.44 0.31 Stock A 0.36 0.20 0.04 Stock B 0.48 0.26 Stock C 0.52 0.12 -0.44 Bust a-1 If your portfolio is invested 40 percent each in A and B and 20 percent in C, what is the portfolio expected return? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal placos.) Portfollo expected return a-2 What is the variance? (Do not round intermediate calculations. Round the final answer to 5 decimal places.) Variance a-3 What is the standard deviaton? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) Standard deviation b. If the expected T-bill rate is 4.80 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter the answer as a percent rounded to 2 decimal places.) Expected risk premium c-1 If the expected infiation rate is 2.80 percent, what are the approximate and exact expected real returns on the portfolio? (Do not round intermediate calculations. Enter the answers as a percent rounded to 2 decimal places) Approxmate expected real return Exact expected real return c-2 What are the approxomate and exact expected real risk premiums en the partfalio? (Do not round intermediate calculations. Enter the answors as a percont rounded to 2 decimal places.) Approximate expected real risk premiumm Exact expected real risk premium

Solution

a-1: Portfolio expected return = sum of (Probability * expected return of state of economy)
Here, expected return of state of economy can be calculated as:
Expected return = sum of (weight * return)
Boom: E(Rp) = 0.40(0.36) + 0.40(0.48) + 0.20(0.52) = 0.3464 or 34.64%
Normal: E(Rp) = 0.40(0.20) + 0.40(0.15) + 0.20(0.12) = 0.164 or 16.4%
Bust: E(Rp) = 0.40(0.04) + 0.40(–0.26) + 0.20(–0.44) = –0.176 or –17.6%

Therefore, Portfolio expected return = sum of (Probability * expected return of state of economy)
= 0.25* 34.64% + 0.44* 16.4% + 0.31* (-17.6%) = 10.42%

a-2: Formula for variance = sum of (Probability * (expected return of state of economy - Portfolio expected return)²
Variance = 0.25(0.3464 – 0.1042)²+ 0.44(0.164 – 0.1042)²+ 0.31(–0.176 – 0.1042)²
= 0.0405774

a-3: Standard deviation = square root of variance
Standard deviation = square root of 0.0405774

= (0.0405774)^1/2 = 0.0202887

b. Expected risk premium = Portfolio expected return - risk free rate
= 10.42% - 4.8% = 5.62%

c-1: Appropriate expected real return = Portfolio expected return - inflation rate
= 10.42% - 2.8%= 7.62%
Exact expected real return (with the help of fisher equation we can find the exact real return):
Equation: 1+ Portfolio expected return= (1+ inflation rare) * (1+ exact real return)
(1+ exact real return) = (1+ Portfolio expected return)/ (1+ inflation rare)
= 1+ 10.42% / 1+2.8%
= 1.1042 / 1.028 = 1.07412
(1+ exact real return) = 1.07412
Exact expected real return = 1.07412 - 1 = 0.07412 = 7.41%

c-2: Appropriate expected real risk premium = Portfolio expected return - risk free rate
= 10.42% - 4.8% = 5.62%
Exact expected real risk premium = Appropriate expected real risk premium / (1+ inflation rate)
= 5.62% / (1+ 2.8%)
= 0.0562 / 1.028 = 0.05467 = 5.47%