You invest in a country named Papaf. You observe the stock returns on a list of stocks during
three periods.
$$\begin{array} { c c c r }
\text { Stack } & \text { Periad 1 } & \text { Periad 2 } & \text { Periad 3 } \
\hline \text { A } & 14.5 \% & - 10.5 \% & 14 \% \
\text { B } & 11 \% & - 6.5 \% & 10.5 \% \
\text { C } & 7.5 \% & - 3 \% & 8 \% \
\text { D } & 5.5 \% & - 1 \% & 5 \% \
\text { E } & 2 \% \% & 2 \% & 2.5 \% \
\text { F } & - 1.5 \% & 5 \% & - 1 \%
\end{array}$$ You consider explaining differences in returns by common factors, with a linear model as represented in Equation (6.9). You have two candidates for factors: movements in interest rates and changes in the local temperature measured at noon-time from the previous day. The various values of these factors are given below:
$\begin{array}{c}
\begin{array}{lll}
\text { Factor}\
\text { Change in Interest Rate }\
\text { Change in Temperature}
\end{array}
\begin{array}{lll}
\text { Period 1}\
-3 \% \
-5 \%
\end{array}
\begin{array}{lll}
\text { Period 2}\
+3 \% \
-3 \%

\end{array}
\begin{array}{lll}
\text { Period3}\
-3 \% \
+5 \%

\end{array}
\end{array}$
a. Try to assess whether each factor has an influence on stock returns.
b. Try to estimate the intercept and the factor exposures of each asset.

Question

You invest in a country named Papaf. You observe the stock returns on a list of stocks during
three periods.
 $$\begin{array} { c c c r } 
\text { Stack } & \text { Periad 1 } & \text { Periad 2 } & \text { Periad 3 } \
\hline \text { A } & 14.5 \% & - 10.5 \% & 14 \% \
\text { B } & 11 \% & - 6.5 \% & 10.5 \% \
\text { C } & 7.5 \% & - 3 \% & 8 \% \
\text { D } & 5.5 \% & - 1 \% & 5 \% \
\text { E } & 2 \% \% & 2 \% & 2.5 \% \
\text { F } & - 1.5 \% & 5 \% & - 1 \%
\end{array}$$ You consider explaining differences in returns by common factors, with a linear model as represented in Equation (6.9). You have two candidates for factors: movements in interest rates and changes in the local temperature measured at noon-time from the previous day. The various values of these factors are given below:
 $\begin{array}{c}
\begin{array}{lll}
 \text { Factor}\
 \text { Change in Interest Rate }\
 \text { Change in Temperature}
\end{array}
\begin{array}{lll}
 \text { Period 1}\
-3 \% \
-5 \%
\end{array}
\begin{array}{lll}
 \text { Period 2}\
+3 \% \
-3 \%
 
\end{array}
\begin{array}{lll}
 \text { Period3}\
-3 \% \
+5 \%
 
\end{array}
\end{array}$
 a. Try to assess whether each factor has an influence on stock returns.
b. Try to estimate the intercept and the factor exposures of each asset.

Quizplus · Accepted Answer

The Answer is a. The model is:

R _ { i } = \alpha _ { i } + \beta _ { 1 i } f _ { 1 } + \beta _ { 2 i } f _ { 2 } + \varepsilon _ { i }

where:

R _ { i }

is the return on stock i

f _ { 1 }

is the factor "change in interest rate"

f _ { 2 }

is the factor "change in temperature"

\alpha _ { i }

is the intercept of stock i

\beta _ { 1 i }

is the exposure of stock i to factor 1

\beta _ { 2 i }

is the exposure of stock i to factor 2.
We could use a regression to estimate the exposures. A casual look at the data suggests that the second factor has no (or little) influence on stock returns

\left( \beta _ { 2 i } = 0 \right)

b. The intercept and exposure to the first factor are estimated approximately at:

\alpha = 2 \%

for all stocks

\beta _ { L A } = - 4

\beta _ { 1 B } = - 3

\beta _ { 1 C } = - 2

\beta _ { 1 D } = - 1

\beta _ { 1 z } = 0

\beta _ { 1 \boldsymbol { F } } = + 1

You Invest in a Country Named Papaf You Consider Explaining Differences in Returns by Common Factors, with Stock