2011 GARP Practice paper

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Hi David,

Just not able to understand the below question from 2011 GARP practice questions. Could you pls help. What does the t mean (t = 4.40) (t = 12.1). If you have analysed this question before, could you pls direct me to the link.

Thanks,

Laksh

19. Rick Masler is considering the performance of the managers of two funds, the HCM Fund and the GRT Fund.
He uses a linear regression of each manager’s excess returns (ri) against the excess returns of a peer group (rB):
ri = ai + bi * rB + εi
The information he compiles is as follows:



Fund Initial Equity Borrowed Funds Total Investment Pool ai bi
HCM USD 100 USD 0 USD 100 0.0150 0.9500
(t = 4.40) (t = 12.1)
GRT USD 500 USD 3,000 USD 3,500 0.0025 3.4500
(t = 0.002) (t = 10.20)

Based on this information, which of the following statements is correct?
a. The regression suggests that both managers have greater skill than the peer group.
b. The ai term measures the extent to which the manager employs greater or lesser amounts of leverage
than do his/her peers.
c. If the GRT Fund were to lose 10% in the next period, the return on equity (ROE) would be -60%.
d. The sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.
Answer: d.
Explanation:
Statement d is correct as can be seen from the bi coefficient. It is higher for GRT and lower for HCM. This indicates
that the sensitivity of the GRT fund to the benchmark return is much higher than that of the HCM fund.
Topic: Risk Management and Investment Management
Subtopic: Risk decomposition and performance attribution
AIMS: Describe common features of a performance measurement framework including comparisons with benchmark
portfolios and peer groups
Reference: Robert Litterman and the Quantitative Resources Group, Modern Investment Management: An
Equilibrium Approach (Hoboken, NJ: John Wiley & Sons: 2003). Chapter 17—Risk Monitoring and Performance
Measurement

 

[David Harper CFA FRM]

Hi Laksh,

(I don't think we've yet analyzed this question)

The numbers are maybe more familiar if the standard errors are included. The "t" are the computed t values = regression coefficient / standard error; so, standard error = regression coefficient / computed t and a more complete display could be (with respect to HCM):

r(i) = 0.0150 + 0.9500*r(b)
se= (0.0034) (0.0785)
t = (4.40) (12.1)

So, 12.1 is the number of standard deviations (errors) that 0.95 (the coefficient) is from zero (the null hypothesis for the coefficient). The larger this t, the less likely this difference (i.e., between 0.95 and 0) is due to sampling variation. For large sample (n-1 = df), generally computed t >> 2.0 or 3.0 is significant. In this case, high t values imply the slope coefficients (both HCM and GRT) are significantly different than zero.

But the "sensitivity" is given by the beta (the regression coefficient) itself.

For example, if everything were the same on this question, except change t = 10.20 to t = 0.80 (i.e., below 2.0), then we could say HCM is "more sensitive" because the beta for GRT is not statistically significant.

We might think of a high t value as akin to "okay, this coefficient is going to be considered" and a low t as akin to "regardless of the value, we can't use it."

Hope that helps, David