Question

In: Finance

What is the expected return, standard deviation, and CV for each of these stocks? Which offers...

What is the expected return, standard deviation, and CV for each of these stocks? Which offers you the best risk/reward ratio?

Prob.		Alpha	Beta
0.2	Great	22%	31%
0.4	Average	12%	15%
0.2	Poor	-5%	-10%
0.2	Catastrophic	-15%	-20%

Expert Solution

Answer :-

Expected reurn of Alpha

5.2% or 0.052

Expected reurn of Alpha

6.2%

Standard deviation of Alpha= 0.1673878

Standard deviation of Beta = 0.233906

Co variance of Alpha =3.2189

Co variance of Beta = 3.7726774

..

Explanation :-

Calculation of the Expected return of the Stock

Expected Return of alpha
Particulars	Probability (A)	Return (B)	Expected Return (A × B)
Great	0.20	22%	4.4%
Avarage	0.40	12%	4.8%
Poor	0.20	-5%	-1%
Catastrophic	0.20	-15%	-3%
Expected reurn of Alpha	5.2% or 0.052

Expected Return of Beta
Particulars	Probability (A)	Return (B)	Expected Return (A × B)
Great	0.20	31%	6.2%
Avarage	0.40	15%	6%
Poor	0.20	-10%	-2%
Catastrophic	0.20	-20%	-4%
Expected reurn of Alpha	6.2%

..

Calculation of standard deviation

Standard Deviation of Alpha
Return(R)	Expected Return(ER)	R-ER	(R-ER)^2
0.22	0.052	0.168	0.028224
0.12	0.052	0.068	0.004624
-0.05	0.052	-0.102	0.010404
-0.15	0.052	-0.202	0.040804
Total (R-ER)^2	0.084056

..

Standard Deviation =

n= size / number of return = 4

=

Standard deviation of Alpha= 0.1673878

.

Standard Deviation of Beta
Return(R)	Expected Return(ER)	R-ER	(R-ER)^2
0.31	0.062	0.248	0.061504
0.15	0.062	0.088	0.007744
-0.10	0.062	-0.162	0.026244
-0.20	0.062	-0.262	0.068644
Total (R-ER)^2	0.164136

.

Standard Deviation =

n= size / number of return = 4

Standard deviation =

=

Standard deviation of Beta = 0.233906

..

Covariance of Stocks

Covariance = Standard deviation / Mean (Expected Return)

Covariance of Alpha

Expected return of Alpha = 0.052

Standard deviation of Alpha = 0.1673878

Covariance = 0.1673878 / 0.052

Co variance of Alpha =3.2189

Covariance of Beta

Expected return of Alpha = 0.062

Standard deviation of Alpha = 0.233906

Covariance =0.233906 / 0.062

Co variance of Beta = 3.7726774

Alpha is the best risk reward ratio

jeff jeffy answered 2 years ago

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