Question

Fill in the remaining entries in the following table using the formulas for the expected return and the variance of a portfolio below. Please show your detailed calculations or provide arguments to support your answers. I will not be able to give you full credit even if your answer is correct.

Allocation to Stock	Allocation to Bond	Portfolio Mean	Portfolio Std Dev
0%	100%	10.0%	10.00%
25%	75%
50%	50%		12.85%
75%	25%
100%	0%	15.0%	20.00%

Answer 1

Solution:
Allocation to Stock	Allocation to Bond	Portfolio Mean	Portfolio Std Dev
0%	100%	10.00%	10.00%
25%	75%	11.25%	10.55%
50%	50%	12.50%	12.85%
75%	25%	13.75%	16.17%
100%	0%	15.00%	20.00%
Working Notes:
1.From the above sheet we can see that when 100% is allocated to bond Portfolio Mean and SD is 10% and 10% respectively.
2.Also, when 100% is allocated to Stock Portfolio Mean and SD is 15% and 20% respectively.
Hence from the above two Points we can conclude that Return and SD of Bond is 10% and 10% respectively.
Also, Return and SD of Stock is 15% and 20% respectively
So we can calculate the Portfolio mean using the following formula:
Ws*Rs+Wb*Rb
Where Ws= Weight of Stock
Rs = Return of Stock
For example where Stock Allocation is 25% and Bond Allocation is 75%, portfolio mean is
25%*15%+75%*10%=	11.25%
All other Portfolio means can be calculated like above.
3. Lets Come to the Portfolio SD part
Now the formula for calculating portfolio SD is:
[(Ws)2*(SDs)2+(Wb)2*(SDb)2+2*Ws*Wb*SDs*SDb*Rsb]1/2
Where
Ws=	Weight of Stock	(Same for Bond)
SDs=	SD of Stock	(Same for Bond)
Rsb=	Correlation Coefficient of Stock and Bond
Correlation Coefficient is a relative measure of co variance between two securites.
Covariance is the co movement of two securities i.e how often they move up and down together.
Now as we can see Portfolio SD is given as 12.85 where weight of both stock and Bond is 50%
we can calculate the value of Rsb as below
(0.50)2*(20)2+(0.50)2*(.10)2+2*0.50*0.50*10*20*Rsb=		(12.85)2
Which gives Rsb=		0.40
With formula given above and value of Rsb with us we can calculate portfolio SD for all other Combinations
Eg
Where allocation of stock is 75% and bond is 25% respectively
[(0.75)2*(20)2+(0.25)2*(.10)2+2*0.50*0.50*10*20*.40]1/2=		16.17%
Same way we can calculate all other combinations
Hope this answers the Question.
Good Luck!