Application Chapter 6 - 9

Question 1

Using the CAPM equation, when the risk-free rate is 2.5%, the expected return of the market is 12%, and the beta of asset i is 1.5, what is the expected return of asset i?

Answer 1

E(R(i)) = R(f) + Beta (E(R(m)) - R(f))

0.025 + 1.5 (0.12 - 0.025) = 0.1675 (16.75%)

Question 2

Using the CAPM equation, when the risk-free rate is 2%, the expected return of the market is 10%, and the beta of asset i is 1.25, what is the expected return of asset i?

Answer 2

E(R(i)) = R(f) + Beta (E(R(m)) - R(f))

0.02 + 1.25 (0.1 - 0.02) = 0.12

Question 3

Using the CAPM equation, when the risk-free rate is 3%, the expected return of the market is 15%, and the beta of asset i is 2, what is the expected return of asset i?

Answer 3

E(R(i)) = R(f) + Beta (R(E(m)) - R(f))

0.03 + 2 (0.15 - 0.03) = 0.27 (or 27%)

Question 4

Using the CAPM equation, when the risk-free rate is 4%, the expected return of the market is 20%, and the beta of asset i is 2.25, what is the expected return of asset i?

Answer 4

E(R(i)) = R(f) + Beta (R(E(m) - R(f))

0.04 + 2.25 (0.20 - 0.04) = 0.4 (or 40%)

Question 5

Using the CAPM equation, when the risk-free rate is 2%, the expected return of the market is 25%, and the beta of asset i is 1, what is the expected return of asset i?

Answer 5

E(R(i)) = R(f) + Beta (E(R(m)) - R(f))

0.02 + 1 (0.25 - 0.02) = 0.25 (or 25%)

Question 6

Using the CAPM equation, when the risk-free rate is 1.5%, the expected return of the market is 15%, and the beta of asset i is 1.15, what is the expected return of asset i?

Answer 6

E(R(i)) = R(f) + Beta (R(E(m)) - R(f))

0.015 + 1.15 (0.15 - 0.015) = 0.17025 (or 17.03%)

Question 7

Using the CAPM equation, when the risk-free rate is 2.5%, the expected return of the market is 10%, and the beta of asset i is 0.5, what is the expected return of asset i?

Answer 7

E(R(i)) = R(f) + Beta (E(R(m) - R(f))

0.025 + 0.5 (0.10 - 0.025) = 0.0625 (or 6.25%)

Question 8

Risk-free rate is 2% and the beta of asset i is 1.25, if the action return of the market is 22%, the ex post CAPM model would generate a return due to non-idiosyncratic effects of:

Then if the asset’s actual return is 30%, then the what would be attributable to idiosyncratic return, E(it):

Answer 8

R(it) = R(f) + Beta (R(mt) - R(f) + E(it)

(it) asset i in time period.

2% + 1.25(22% - 2%) = 0.27

to find the idiosyncratic return:
0.3 - 0.27 = 0.03

Question 9

Risk-free rate is 2.5% and the beta of asset i is 1.5, if the action return of the market is 12%, the ex post CAPM model would generate a return due to non-idiosyncratic effects of:

Then if the asset’s actual return is 23%, then the what would be attributable to idiosyncratic return, E(it):

Answer 9

R(it) = R(f) + Beta (R(mt) - R(f)) + E(it)

0.025+ 1.5 (0.12 - 0.025) = 0.1675 (or 16.75%)

Idiosyncratic return:
(23% is the actual return)
23% - 16.75% = 6.25%

Question 10

Risk-free rate is 3% and the beta of asset i is 2, if the action return of the market is 15%, the ex post CAPM model would generate a return due to non-idiosyncratic effects of:

Then if the asset’s actual return is 29%, then the what would be attributable to idiosyncratic return, E(it):

Answer 10

R(it) = R(f) + Beta (R(mt) - R(f)) - E(it)

0.03 + 2 (0.15 - 0.03) = 0.27 (27%)

Idiosyncratic return:

29% - 27% = 2%

Question 11

Risk-free rate is 4% and the beta of asset i is 2.25, if the action return of the market is 20%, the ex post CAPM model would generate a return due to non-idiosyncratic effects of:

Then if the asset’s actual return is 22%, then the what would be attributable to idiosyncratic return, E(it):

Answer 11

R(it) = R(f) + Beta (R(mt) - R(f)) - E(it)

0.04 + 2.25 (0.20 - 0.04) = 0.4 (40%)

Idiosyncratic return:

22% - 40% = -18%

Question 12

Risk-free rate is 2% and the beta of asset i is 1, if the action return of the market is 25%, the ex post CAPM model would generate a return due to non-idiosyncratic effects of:

Then if the asset’s actual return is 41%, then the what would be attributable to idiosyncratic return, E(it):

Answer 12

R(it) = R(f) + Beta (R(mt) - R(f)) - E(it)

0.02 + 1 (0.25 - 0.02) = 0.25 (or 25%)

Idiosyncratic return:

41% - 25% = 16%

Question 13

Risk-free rate is 1.5% and the beta of asset i is 1.15, if the action return of the market is 15%, the ex post CAPM model would generate a return due to non-idiosyncratic effects of:

Then if the asset’s actual return is 28.30%, then the what would be attributable to idiosyncratic return, E(it):

Answer 13

R(it) = R(f) + Beta

Question 14

A researcher wishes to test for statistically
significant factors in explaining asset returns. Using a confidence level of 90%,
how many statistically significant factors would the researcher expect to identify
by testing 50 variables, independent from one another, that had no true
relationship to the returns?

What if research were performed with a confidence level of
99.9% but with 100 researchers, each testing 50 different variables on different
data sets?

Answer 14

You are searching for the probability of a mistake.

1 researcher conducting the test with a 90% confidence level.

(1 - 0.9) x 50 = 5

If there are 100 researchers conducting the test with a 99.9% confidence level

(((1 - 0.999) x 50) x 100) = 5

Question 15

20 researchers wishes to test for statistically
significant factors in explaining asset returns. Using a confidence level of 95%,
how many statistically significant factors would the researchers expect to identify
by testing 100 variables, independent from one another, that had no true
relationship to the returns?

What if research were performed with a confidence level of
90% but with 25 researchers, each testing 35 different variables on different
data sets?

Answer 15

1 - 0.95 = 0.05

0.05 x 100 = 5

20 x 5 = 100

1 - 0.9 = 0.1

0. 1 x 35 = 3.5
1. 5 x 25 = 87.5

Question 16

20 researchers wishes to test for statistically
significant factors in explaining asset returns. Using a confidence level of 95%,
how many statistically significant factors would the researchers expect to identify
by testing 100 variables, independent from one another, that had no true
relationship to the returns?

What if research were performed with a confidence level of
90% but with 25 researchers, each testing 35 different variables on different
data sets?

Answer 16

1 - 0.95 = 0.05

0.05 x 100 = 5

20 x 5 = 100

1 - 0.9 = 0.1

0. 1 x 35 = 3.5
1. 5 x 25 = 87.5

Question 17

Nine-month riskless securities trade for $97,000,
and 12-month riskless securities sell for $P (both with $100,000 face values and
zero coupons). A forward contract on a three-month, riskless, zero-coupon bond,
with a $100,000 face value and a delivery of nine months, trades at $99,000.
What is the arbitrage-free price of the 12-month zero-coupon security (i.e., P)?

Answer 17

100,000/P = 100,000/97,000)(100,000/99,000)

100,000/P = 1.041341

P = 100,000/1.041341

P = 96,030.00

Therefore, the 12-month bond must sell for $96,030.00 to prevent arbitrage.

Question 18

Nine-month riskless securities trade for $98,000,
and 12-month riskless securities sell for $P (both with $100,000 face values and
zero coupons). A forward contract on a three-month, riskless, zero-coupon bond,
with a $100,000 face value and a delivery of nine months, trades at $98,980.
What is the arbitrage-free price of the 12-month zero-coupon security (i.e., P)?

Answer 18

100,000/P = (100,000/98,000)(100,000/98,980)

$97,000.40

Question 19

A three-year riskless security trades at a yield of
3.4%, whereas a forward contract on a two-year riskless security that settles in
three years trades at a forward rate of 2.4%. Assuming that the rates are
continuously compounded, what is the no-arbitrage yield of a five-year riskless
security?

Answer 19

F(T-t) = (T x R(T) - t x R(t)) / (T - t)

manipulation:

F (T-t) x (T - t) = (T x R(T) - t x R(t))

F(T-t) x (T - t) + t R(t) = T x R(T)

R(T) = F(T-t) x (T - t) + t x R / T

R(t) = 3.4% 
F(T-t) = 2.4% 
T = 5 
t = 3 

R(T) = 0.024% x (5 - 3) + 3 x 0.034% / 5 = 0.03 (3%)

Question 20

A three-year riskless security trades at a yield of
3.4%, whereas a forward contract on a two-year riskless security that settles in
three years trades at a forward rate of 2.4%. Assuming that the rates are
continuously compounded, what is the no-arbitrage yield of a five-year riskless
security?

Answer 20

F(T-t) = (T x R(T) - t x R(t)) / (T - t)

manipulation:

F (T-t) x (T - t) = (T x R(T) - t x R(t))

F(T-t) x (T - t) + t (R(t)) = T x R(T)

R(T) = F(T-t) x (T - t) + t x R(t) / T

R(t) = 3.4% 
F(T-t) = 2.4% 
T = 5 
t = 3 

R(T) = 0.024% x (5 - 3) + 3 x 0.034% / 5 = 0.03 (3%)

Question 21

A three-year riskless security trades at a yield of
7%, whereas a forward contract on a two-year riskless security that settles in
three years trades at a forward rate of 5%. Assuming that the rates are
continuously compounded, what is the no-arbitrage yield of a five-year riskless
security?

Answer 21

F(T-t) = (T x R(T) - t x R(t)) / (T - t)

manipulation:

F(T-t) x (T - t) = T x R(T) - t x R(t)

(F(T-t) x (T - t)) + (t x R(t) = T x R(T)

R(T) = (F(T-t) x (T-t)) + (t x R(t)) / T

R(T-t) = 0.05% 
R(t) = 0.07% 
T = 5 
t = 3 

R(T) = (0.05 x (5-3)) + 3 x 0.07 / 5 = 0.062 (6.2%)

Question 22

A three-year riskless security trades at a yield of
3.3%, whereas a forward contract on a two-year riskless security that settles in
three years trades at a forward rate of 1.5%. Assuming that the rates are
continuously compounded, what is the no-arbitrage yield of a five-year riskless
security?

Answer 22

F(T-t) = (T x R(T) - t x R(t) / (T - t)

manipulation:

F(T-t) x (T - t) = (T x R(T) - t x R(t))

R(T) = F(T-t) x (T - t) + t x R(t) / T

F(T-t) = 1.5% 
R(t) = 3.3% 
T = 5 
t = 3

R(T) = 0.015% x (5 - 3) + 3 x 0.033 / 5 = 0.0258 (2.58%)

Question 23

A stock currently selling for $10 will either rise to
$30 or fall to $0 in one year. How much would a one-year call sell for if its strike
price were $20?

Answer 23

Future price - Strike price

30 - 20 = $10

$10(pay off call) / $30 (future stock price) = 1/3

0.33333 x $10 (current stock price) = $3.33

$3.33 is the price of the call.

Question 24

A stock currently selling for $10 will either rise to
$100 or fall to $0 in one year. How much would a one-year call sell for if its strike
price were $40?

Answer 24

the potential/future price - the strike price

$100 - $40 = $60

/ future price
$60 / $100 = 0.6

x current price
0.6 x $10 = $6

Question 25

A stock currently selling for $20 will either rise to
$50 or fall to $0 in one year. How much would a one-year call sell for if its strike
price were $25?

Answer 25

future price - strike price
$50 - $25 = $25

pay of call price / future price
25 / 50 = 0.5

x current price
20 x 0.5 = $10

Question 26

A stock sells for $100 and is certain to make a
cash distribution of $2 just before the end of one year. A forward contract on that
stock trades with a settlement in one year. Assume that the cost to finance a
$100 purchase of the stock is $5 (due at the end of the year). What is the noarbitrage
price of this forward contract?

Answer 26

Stock price grows at 5% riskless rate (ignoring the dividend).

We need to pay $100 in the spot market for the stock.

To finance the purchase it costs $5, so purchase stock in the spot market and hold it one year costs $105.

However, the stock will distribute a $2 dividend to investors, making the actual costs $105 - $2 = $103

The cost of purchasing the stock in the spot market is $103 so the forward contract, which settles in $100 worth of the stock in one year should trade at the same price to prevent arbitrage.

$100 + $5 = $105

105 - $2 = $103

Question 27

A stock sells for $100 and is certain to make a
cash distribution of $2 just before the end of one year. A forward contract on that
stock trades with a settlement in one year. Assume that the cost to finance a
$100 purchase of the stock is $5 (due at the end of the year). What is the no-arbitrage
price of this forward contract?

Answer 27

Stock price grows at 5% riskless rate (ignoring the dividend).

We need to pay $100 in the spot market for the stock.

To finance the purchase it costs $5, so purchase stock in the spot market and hold it one year costs $105.

However, the stock will distribute a $2 dividend to investors, making the actual costs $105 - $2 = $103

The cost of purchasing the stock in the spot market is $103 so the forward contract, which settles in $100 worth of the stock in one year should trade at the same price to prevent arbitrage.

$100 + $5 = $105

105 - $2 = $103

Question 28

A stock sells for $50 and is certain to make a
cash distribution of $3 just before the end of one year. A forward contract on that
stock trades with a settlement in one year. Assume that the cost to finance a
$50 purchase of the stock is $6 (due at the end of the year). What is the no-arbitrage
price of this forward contract?

Answer 28

Add the purchase cost:
$50 + $6 = $56

Take away the dividend:
$56 - $3 = $53

Question 29

A stock sells for $75 and is certain to make a
cash distribution of $0 just before the end of one year. A forward contract on that
stock trades with a settlement in one year. Assume that the cost to finance a
$75 purchase of the stock is $2 (due at the end of the year). What is the no-arbitrage
price of this forward contract?

Answer 29

Add the cost of purchase:
$75 + $2 = $77

Take away the dividend:
$77 - $0 = $77

Question 30

If the spot price of an equity index that pays no
dividends is $500 and if the riskless interest rate is zero, what is the one-year
forward price on the equity index?

Answer 30

Riskless rate - dividend

0% - 0% = 0%

x 1

2nd > e^(x)

x 500

= $500

Question 31

If the spot price of an equity index that pays 5.0%
dividends is $250 and if the riskless interest rate is 5%, what is the one-year
forward price on the equity index?

Answer 31

Riskless rate - dividends

0.05% - 0.05% = 0%

x 1

2nd e^(x)

x 250

= $250

Question 32

If the spot price of an equity index that pays 2% is $100 and if the riskless interest rate is 3%, what is the one-year
forward price on the equity index?

Answer 32

riskless rate - dividend

0.03% - 0.02% = 0.01%

x 1 = 0.01%

2n^(x) = 1.010050

x $100 = $101.01

Question 33

If the spot price of an equity index that pays 4% is $50 and if the riskless interest rate is 2%, what is the one-year
forward price on the equity index?

Answer 33

riskless rate - dividend

0.02% - 0.04% = -0.02%

x 1 = -0.02%

2nd e^(x) = 0.980199

x 50 = 49.009934

$49.01

Question 34

If the spot price of an equity index that pays 2% dividends is $100 and if the riskless interest rate is 3%, what is the one-year
forward price on the equity index?

Answer 34

riskless rate - dividend

0.03% - 0.02% = 0.01%

x 1 = 0.01%

2n^(x) = 1.010050

x $100 = $101.01

Question 35

If the spot price of an equity index that pays 4% dividends is $50 and if the riskless interest rate is 2%, what is the one-year
forward price on the equity index?

Answer 35

riskless rate - dividend

0.02% - 0.04% = -0.02%

x 1 = -0.02%

2nd e^(x) = 0.980199

x 50 = 49.009934

$49.01

Question 36

If the spot price of an equity index that pays no
dividends is $500 and if the riskless interest rate is zero, what is the one-year
forward price on the equity index?

Answer 36

Riskless rate - dividend

0% - 0% = 0%

x time (annual = 1, semiannual = 0.5, 3-months = 0.025)
x 1 

2nd > e^(x)

x 500

= $500

Question 37

If the spot price of an equity index that pays 5.0%
dividends is $250 and if the riskless interest rate is 5%, what is the one-year
forward price on the equity index?

Answer 37

Riskless rate - dividends

0.05% - 0.05% = 0%

x time (annual = 1, semiannual = 0.5, 3-months = 0.025)
x 1 

2nd e^(x)

x 250

= $250

Question 38

If the spot price of an equity index that pays 2% dividends is $100 and if the riskless interest rate is 3%, what is the one-year
forward price on the equity index?

Answer 38

riskless rate - dividend

0.03% - 0.02% = 0.01%

x time (annual = 1, semiannual = 0.5, 3-months = 0.025)
x 1 = 0.01% 

2n^(x) = 1.010050

x $100 = $101.01

Question 39

If the spot price of an equity index that pays 4% dividends is $50 and if the riskless interest rate is 2%, what is the one-year
forward price on the equity index?

Answer 39

riskless rate - dividend

0.02% - 0.04% = -0.02%

x time (annual = 1, semiannual = 0.5, 3-months = 0.025)
x 1 = -0.02% 

2nd e^(x) = 0.980199

x 50 = 49.009934

$49.01

Question 40

Assuming a continuously compounded annual
interest rate of 5%, if the spot price of an equity index with 2% dividends is $500,
what would be the forward price on the equity index with settlement in three
months?

Six months?

Twelve months?

Answer 40

e^(r-d)(T)

500e^(0.05%-0.03%)(0.25)

0.05% - 0.03% = 0.02%

x time (annual = 1, semiannual = 0.5, 3-months = 0.025)
x 0.25 = 0.005

2nd e^(x) = 1.005013

x 500 = $502.51

Question 41

Assuming a continuously compounded annual
interest rate of 5%, if the spot price of an equity index with 2% dividends is $500,
what would be the forward price on the equity index with settlement in six
months?

Answer 41

500e^(r - d)(T)

500e^(0.05%-0.02%)(0.5)

0.05 - 0.02 = 0.03

x 0.5 = 0.015

2nd e^(x) = 1.015113

x 500 = 507.556532

$507.56

Question 42

Assuming a continuously compounded annual
interest rate of 5%, if the spot price of an equity index with 2% dividends is $500,
what would be the forward price on the equity index with settlement in twelve
months?

Answer 42

500e^(r - d)(T)

500e^(0.05-0.02)(1)

0.05 - 0.02 = 0.03

x 1 = 0.03

2nd e^(x) = 1.030455

x 500 = 515.227267

$515.23

Question 43

Assuming a continuously compounded annual
interest rate of 2%, if the spot price of an equity index with 3% dividends is $500,
what would be the forward price of a contract with settlement in three months?

Answer 43

500e^(r - d)(T)

500e^(0.02-0.03)(0.25)
(r - d) will be a negative value.

0.02 - 0.03 = -0.01

x 0.25 = -0.0025

2nd e^(x) = 0.997503

x 500 = 498.751561

$498.75

Question 44

Find the systematic and idiosyncratic returns for
the following: Assume that the risk-free rate is 2%, the realized return of asset i in
year t was 16%, the realized return of the market portfolio was 14% (which was
12% more than the riskless rate), and the beta of asset i is 1.25.

Answer 44

R(it) - R(f) = Beta(i) (R(mt) + R(f)) + E(it)

0.16% - 0.02% = 1.25(0.14% - 0.02%) + E(it)

= -0.01 (-1%)

Question 45

Find the systematic and idiosyncratic returns for
the following: Assume that the risk-free rate is 3%, the realized return of asset i in
year t was 25%, the realized return of the market portfolio was 10% (which was
7% more than the riskless rate), and the beta of asset i is 1.

Answer 45

R(it) - R(f) = Beta(i) (R(mt) + R(f)) + E(it)

0. 25% - 0.03% = 1 (0.10% - 0.03) + E(it)
1. 15 or (15%)

Question 46

Find the systematic and idiosyncratic returns for
the following: Assume that the risk-free rate is 2.5%, the realized return of asset i in
year t was 10%, the realized return of the market portfolio was 15% (which was
12.5% more than the riskless rate), and the beta of asset i is 1.3.

Answer 46

R(it) - R(f) = Beta(i) (R(mt) - R(f)) - E(it)

0. 10% - 0.025 = 1.3(0.15 - 0.025) + E(it)
   - 0.08750 (or -8.75%)

Question 47

Consider Sludge Fund, a fictitious fund run by
unskilled managers that generally approximates the S&P 500 Index but does so
with an annual expense ratio of 100 basis points (1%) more than other
investment opportunities that mimic the S&P 500. Using Equation 8.1 and
assuming that the S&P 500 is a proxy for the market portfolio, the ex ante alpha
of Sludge Fund would be approximately –100 basis points per year. This can be
deduced from assuming that βi = 1 and that [E(Ri,t) – E(Rm,t)] = –1% due to the
expense ratio. Sludge Fund could be expected to offer an ex ante alpha,
meaning a consistently inferior risk-adjusted annual return, of?

Answer 47

E(R(it) - R(f)) = alpha(i) + Beta(i) (E(R(mt) - R(f))

manipulation to find alpha:

Alpha(i) = Beta(i) (E(R(mt) - R(f)) - E(R(it -ExpenseRatio - R(f))

the expected market return and the expected fund return are the same. However, the fund has 1% expense ratio.

Alpha (i) = 1(0.1 - 0) - (0.1 + 0.01 - 0)
= 0.1 - 0.11
= - 0.01 (-1%)

Alpha (i) = 1(2 - 0) - (2 + 0.01 - 0)
= 2 - 2.01
= -0.01 (-1%)

Question 48

Consider Trim Fund, a fund that tries to mimic
the S&P 500 Index and has managers who are unskilled. Unlike Sludge Fund
from the previous section, Trim Fund has virtually no expenses. Although Trim
Fund generally mimics the S&P 500, it does so with substantial error due to the
random incompetence of its managers. However, the fund is able to maintain a
steady systematic risk exposure of βi = 1. Last year, Trim Fund outperformed the
S&P 500 by 125 basis points. Using Equation 8.2, assuming that βi = 1 and that
(Rit – Rmt) = +1.25%, it can be calculated that ε(it) =

Answer 48

R(it) - R(f) = Beta(i) (R(mt) - R(f)) + E(it)

Rearrange E(it):

E(it) = R(it) - R(f) / Beta - R(mt) + R(f)

R(it) - R(mt) = 1.25% 
Beta = 1 
R(it) = 11.25% 
R(mt) = 10%
R(f) = 0

11.25 - 0 / 1 - 10 + 0 = 0.125

Question 49

Consider a regression with an alpha estimate of
0.5% (with a standard error of 0.3) and a beta estimate of 1.1 (with a standard
error of 0.3). Are the regression parameters statistically significant?

At a 5%
significance level (Note: the significance level is 5%, the confidence interval is
95%), the t-statistic needs to exceed 1.96 to be deemed statistically significant
(assuming a very large number of degrees of freedom).

Answer 49

T-statistic = Alpha or Beta / standard error

T-statistic Beta = 1.1/0.3 = 3.67

T-statistic Alpha = 0.5/0.3 = 1.67

0 < > 1.96

t-statistic < Z-Score; not deemed to be significantly different from zero

Alpha estimate is not deemed statistically significant, as it is less than the value of 1.96.

t-statistic > Z-Score; does differ significantly from zero

Beta estimate is deemed statistically significant, as it has value greater than the 1.96 z-score.

Question 50

Consider a regression with an alpha estimate of
0.5% (with a standard error of 0.3) and a beta estimate of 1.1 (with a standard
error of 0.3). Are the regression parameters statistically significant?

At a 5%
significance level (Note: the significance level is 5%, the confidence interval is
95%), the t-statistic needs to exceed 1.96 to be deemed statistically significant
(assuming a very large number of degrees of freedom).

Answer 50

T-statistic = Alpha or Beta / standard error

T-statistic Beta = 1.1/0.3 = 3.67

T-statistic Alpha = 0.5/0.3 = 1.67

0 < > 1.96

t-statistic < Z-Score; not deemed to be significantly different from zero

Alpha estimate is not deemed statistically significant, as it is less than the value of 1.96.

t-statistic > Z-Score; does differ significantly from zero

Beta estimate is deemed statistically significant, as it has value greater than the 1.96 z-score.

Question 51

Consider a regression with an alpha estimate of
0.5% (with a standard error of 0.3) and a beta estimate of 1.1 (with a standard
error of 0.3). Are the regression parameters statistically significant?

At a 10%
significance level (Note: the significance level is 10%, the confidence interval is
90%), the t-statistic needs to exceed 1.65 to be deemed statistically significant
(assuming a very large number of degrees of freedom).

Answer 51

t-statistic: Beta or Alpha / standard error

Alpha:

0.5/0.3 = 1.666667

which is greater than the z-score, meaning the alpha estimate is significant.

Beta:

1.1/0.3 = 3.666667

which is greater than the z-score 1.65. So the beta estimate is also significant.

Question 52

A 50-week rolling window analysis is performed
with exactly four years of data (208 weeks). How many analyses would be
performed, and how many statistically independent analyses would there be?

Answer 52

Number of windows of analyses is:
four years of data (208 weeks) - the number of weeks in the rolling window analysis (50)
208 - 50 = 158

The number of statistically independent analyses would be:
the amount of time (f years/208 weeks / the 50 rolling week analysis
208/50 = 4.16 (4)

Question 53

A 25-week rolling window analysis is performed
with more than four years of data (300 weeks). How many analyses would be
performed, and how many statistically independent analyses would there be?

Answer 53

Number of analyses performed:
300-25 = 275

Number of statistically independent analyses:
300/25 = 12