## Quants Revision

pankaj.pankster
Posts: 2
Joined: Thu Jun 02, 2016 6:08 am

### Quants Revision

Hi ,

The explanation is not clear for the questions from the revision deck .These are question number 16 , 22 and 32

Consider two stocks A and B. Assume their annual returns are jointly normally distributed, the
marginal distribution of each stock has mean 2% and standard deviation 10%, and the correlation is
0.9. What is the expected annual return of stock A if the annual return of stock B is 3%?
A. 2.9%
B. 2%
C. 1.1%
D. 4.7%

Which of the following statements about the linear regression of the return of a portfolio over the
return of its benchmark presented below are correct?
Portfolio parameter Value
Beta 1.25
Alpha 0.26
Coefficient of determination 0.66
Standard deviation of error 2.42
I. The correlation is 0.71
II. 34% of the variation in the portfolio return is explained by variation in the benchmark return
III. The portfolio is the dependent variable
IV. For an estimated portfolio return of 12%, the confidence interval at 95% is [7.16%;16.84%]
A. II and IV
B. III and IV
C. I, II and III
D. II, III and IV

John is forecasting a stock’s performance in 2010 conditional on the state of the economy of the country in
which the firm is based. He divides the economy’s performance into three categories of “GOOD”, “NEUTRAL”
and “POOR” and the stock’s performance into three categories of “increase”, “constant” and “decrease”. He
estimates:
• The probability that the state of the economy is GOOD is 20%. If the state of the economy is GOOD, the
probability that the stock price increases is 80% and the probability that the stock price decreases is 10%.
• The probability that the state of the economy is NEUTRAL is 30%. If the state of the economy is
• NEUTRAL, the probability that the stock price increases is 50% and the probability that the stock price
• decreases is 30%.
• If the state of the economy is POOR, the probability that the stock price increases is 15% and the probability
that the stock price is 70%.
Billy, his supervisor, asks him to estimate the probability that the state of the economy is NEUTRAL given that
the stock performance is constant. John’s best assessment of that probability is closest to:
A. 15.5%
B. 19.6%
C. 20.0%
D. 38.7%

edupristine
Finance Junkie
Posts: 722
Joined: Wed Apr 09, 2014 6:28 am

### Re: Quants Revision

Hi Pankaj

The first step, is to find the Beta of Stock A with respect to Stock B.
Beta (A) = correlation * std(A)/std(B) = 0.9*10%/10% = 0.9

Now, Return A = Avg A + Beta(A)*[(Return(B) - Avg B]
Return A = 2% + 0.9*(3%-2%)
= 2.9%
the explanation is given below
slope or beta(A with respect to B) is
Slope (A regressed on B) = Beta (A with respect to B) = Covariance(A,B) /Variance(A,B) = correlation(A,B)*StdDev(A)*StdDev(B)/Variance(B) = correlation(A,B)*StdDev(A)/StdDev(B).
Slope (A regressed on B) = 0.9*10%/10% = 0.9
A(i) = intercept + slope*B(i) = 0.2% + 0.9*3%; i.e., this is the regression
A(i) = E[A|B] = A(i) = intercept + slope*B(i) = 0.2% + 0.9*3%
so the calculation is E[A|B=3%] = 0.2% + 0.9*3% = 2.9%