Jensen's Inequality

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David,

Can we expect question from Jensen's Inequality in L1 frm?
If yes, please share some examples.

-snigdha

 

[David Harper CFA FRM]

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.

 

[mdke250]

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

 

[ShaktiRathore]

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

 

[mdke250]

Oh, somehow i read it and got it in my head that .0525 was E(RM) not "market risk premium". Thats for pointing that out, have to read more carefully.