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essaygo
PUBLISHED ON:
2021年12月20日
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Question 1. (10 points; 5 each)

a) The average level of total cholesterol in adults aged 20 or older in United States is 191
mg/dL. Suppose that the level of total cholesterol can be approximated as a normal
distribution, with a standard deviation of 40.8 mg/dL.

According to the American Heart Association, a total cholesterol above 240 mg/dL puts a
person in the high-risk category.

Determine the proportion of Americans in the high-risk category—that is, the proportion
of the population with total cholesterol above 240 (or, the probability that a randomly
chosen person has total cholesterol above 240). For this, write down the Excel formula
(plus parameters) that you would use to compute the probability.

(You do not need to actually compute the probability, but rather how you would be able
to compute it, say using an Excel formula.)

We compute =1- NORM.DIST(240,191,40.8,1) =1 – 0.885=11.5%.

Question 1. (Continued)

b) We rely on CAPM to analyze the performance of the mutual fund “Gala Capital”,
managed by Mr. Smith—a star in the mutual fund industry. Gala Capital is famous for
delivering returns that on average are above the market return.

We collect monthly data between 1985 and 2017 (396 observations) on returns, measured
in percentage terms, and run the regression

Rt – Rft = β0+ β1*( Rmt – Rft) + εt

where Rt is the fund’s return in month t, Rmt is the market return in month t, and Rft is the
risk free rate of return in month t. The regression results show an estimated β0=0.68 (with
a t-statistic=+1.02), estimated β1=1.06 (with a t-statistics=+6.72), and an adjusted-R2 for
the model equal to 73.9%.

Please analyze what explains the performance of Mr. Smith’s fund: whether the
performance comes from his special skills to earn more than what CAPM predicts, from
exposure to risk, or from both sources.

The fund does carry a lot of risk, as evidenced by a significant positive beta. There is
no evidence of special skills to earn more than what is predicted by CAPM, as the alpha
is not significantly different from zero (a t-statistic of +1.02). Thus, the fund’s
performance comes solely from its exposure to risk, as evidenced by the significantly
positive beta.

Question 2. (5 points)

A study relates patterns of CEO compensation and firm performance. It uses quarterly
data for Intel Corp., a total of 441 data points. A basic regression model is tried

COMPENSATIONt=β0+ β1*ROAt-1 + εt

where COMPENSATIONt measures the compensation of Intel CEO (in millions of
dollars) at quarter t and ROAt-1 measures the return on assets for the company in the
previous quarter.

However a concern was raised that the compensation measure may not be stationary.
Your research assistant showed that the pattern of Intel’s CEO compensation over time is
given by the following model:

COMPENSATIONt=γ0 + COMPENSATIONt-1 + εt

Discuss whether you think the time series of compensation is stationary or not. If not
stationary, can you think of a transformation of the compensation measure that would
remove nonstationarity?

Since the coefficient on lagged compensation is equal to 1, this AR(1) process is
nonstationary.

To get a stationary process out of that one can use the first difference,

dYt= Yt – Yt-1

and the process becomes stationary and can be employed in a regression.

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