Two stocks AA and BB have the following attributes: Current Retention Standard S

Question

Two stocks AA and BB have the following attributes: Current Retention Standard Stock: Return on Price: $9.32 $12.87 Deviation: Dividend: $0.65 S0.72 Ratio: 50% 60% 1-Equity 52% 1 5% 63% 18% Compute the RADR for each stock: RADR (AA): RADR (BB): (XXXX%) Based on the RADR, find the CAPM beta for each stock Risk-free rate: 2.5% Market rate: 10.5% Beta (AA): Beta (BB): Based on the beta you found above and assuming a standard deviation for the market of 25%, calculate the amount of uncompensated risk for each security (ie, security standard deviation less the amount of standard deviation associated with compensated risk). Uncompensated risk (AA): _ (xxxx%)

Explanation / Answer

Soln : RADR, risk adjusted return can be calculated by many factors, which is the return of an investment based on certain risk, if comparing 2 securities, they might be having same return but based on what risk involved.

Sharpe ratio is one of the method = (security return - risk free rate)/ standard deviation

Need t calculate first return for AA and BB

For AA , current dividend value = $ 0.65, stock price = $9.32, ROE = 15%, retention ratio, b = 50%

So, growth rate , g = ROE*b = 15%*50% = 7.5%

Stock price = Current dividend *(1+g)/(r-g)

where r = stock return

9.32 = 0.65*(1.075)/(r-0.075), r = 15% (approx.)

Hence, Sharpe ratio = (15% - 2.5%)/52% = 0.24 = RADR

Similarly For stock BB, g = 18%*60% = 10.8%

12.87=0.72*(1.108)/(r-0.108)

r = 17%, Now sharpe ratio = (17%-2.5%)/63% = 0.23 = RADR of BB

Let aa and bb are the betas of the two stocks

Using CAPM model , we can say that, 15% = 2.5 + aa* market premium

13.5 = aa * 8, aa = 1.6875

Similarly 17 = 2.5 + bb* (10.5-2.5) or bb = 14.5/8 = 1.8125

(c) Uncompensated risk, U = standard deviation of security - standard deviation associated with compensated risk

For AA, U = 52% - 25%*1.6875 = 9.81%

For BB , U = 63% - 25%*1.8125 = 17.69%

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.