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David,
Can we expect question from Jensen's Inequality in L1 frm?
If yes, please share some examples.
-snigdha
Can we expect question from Jensen's Inequality in L1 frm?
If yes, please share some examples.
-snigdha
Jensen's Inequality
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Hi snigdha,
You won't be quizzed on Jensen's equality but Jensen's alpha is assigned and, because it merely an application of CAPM, GARP does like to test it. Sample question 2 is copied below from our member forum (source here but annotations are for paid members).
2010 Part 1 sample, Question #2:
Portfolio Q has a beta of 0.7 and an expected return of 12.8%. The market risk premium is 5.25%. The risk-free rate is 4.85%. Calculate Jensen’s Alpha measure for Portfolio Q.
a. 7.67%
b. 2.70%
c. 5.73%
d. 4.27%
[my adds]
2.2. What is the portfolio’s Treynor measure?
2.3. Are Jensen’s and Treynor related?
2.4. What is the portfolio’s Sharpe measure?
2.5. What is a criticism of Jensen’s alpha?
2.6. Is Jensen’s alpha the same as Grinold’s alpha?
Answers:
2. d (4.27% or 4.28%)
Explanation: Jensen’s alpha is defined by:
E(RP ) − RF = αP + βP(E(RM) − RF);
αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 - 0.0485 - 0.7 * (0.0525 + 0.0485 - 0.0485)= 0.0427
a. Incorrect. Forgets to subtract the risk-free rate for the excess market return.
b. Incorrect. Forgets to multiply the excess market return by beta.
c. Incorrect. Forgets to subtract the risk-free rate for both the excess market return and the excess portfolio return.
d. Correct.
Topic: Foundation of Risk Management
Subtopic: Market efficiency, equilibrium and CAPM.
Reference: Amenc and LeSourd, Chapter 4.
You won't be quizzed on Jensen's equality but Jensen's alpha is assigned and, because it merely an application of CAPM, GARP does like to test it. Sample question 2 is copied below from our member forum (source here but annotations are for paid members).
2010 Part 1 sample, Question #2:
Portfolio Q has a beta of 0.7 and an expected return of 12.8%. The market risk premium is 5.25%. The risk-free rate is 4.85%. Calculate Jensen’s Alpha measure for Portfolio Q.
a. 7.67%
b. 2.70%
c. 5.73%
d. 4.27%
[my adds]
2.2. What is the portfolio’s Treynor measure?
2.3. Are Jensen’s and Treynor related?
2.4. What is the portfolio’s Sharpe measure?
2.5. What is a criticism of Jensen’s alpha?
2.6. Is Jensen’s alpha the same as Grinold’s alpha?
Answers:
2. d (4.27% or 4.28%)
Explanation: Jensen’s alpha is defined by:
E(RP ) − RF = αP + βP(E(RM) − RF);
αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 - 0.0485 - 0.7 * (0.0525 + 0.0485 - 0.0485)= 0.0427
a. Incorrect. Forgets to subtract the risk-free rate for the excess market return.
b. Incorrect. Forgets to multiply the excess market return by beta.
c. Incorrect. Forgets to subtract the risk-free rate for both the excess market return and the excess portfolio return.
d. Correct.
Topic: Foundation of Risk Management
Subtopic: Market efficiency, equilibrium and CAPM.
Reference: Amenc and LeSourd, Chapter 4.
Why did you use 0.0485 twice in the last parentheses?
αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 - 0.0485 - 0.7 * (0.0525 + 0.0485 - 0.0485)= 0.0427
it seems from the formula that the following would be correct:
αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 - 0.0485 - 0.7 * (0.0525 - 0.0485)= 0.0767
αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 - 0.0485 - 0.7 * (0.0525 + 0.0485 - 0.0485)= 0.0427
it seems from the formula that the following would be correct:
αP = E(RP ) − RF - βP(E(RM) − RF) = 0.128 - 0.0485 - 0.7 * (0.0525 - 0.0485)= 0.0767
Hi
αP = E(RP ) − RF - βP(E(RM) − RF) => αP = E(RP ) − RF - βP(E(Riskpremium)+RF − RF) since E(RM)=RF+E(RiskPremium), E(RiskPremium)=.0525,RF=.0485 put these values in above formula
Here .0485 is RF so we use it twice in last bracket in above formula.
Thanks
αP = E(RP ) − RF - βP(E(RM) − RF) => αP = E(RP ) − RF - βP(E(Riskpremium)+RF − RF) since E(RM)=RF+E(RiskPremium), E(RiskPremium)=.0525,RF=.0485 put these values in above formula
Here .0485 is RF so we use it twice in last bracket in above formula.
Thanks
Last edited:
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