Question

Calculate the expected return and standard deviation of the following. T.Bills, HT, Coll, USR, MP

Economy	Prob	T.Bills	HT	Coll	USR	MP
Recession	0.1	5.5%	-27.0%	27.0%	6.0%	-17.0%
Below Avg	0.2	5.5%	-7.0%	13.0%	-14.0%	-3.0%
Average	0.4	5.5%	15.0%	0.0%	3.0%	10.0%
Above Avg	0.2	5.5%	30.0%	-11.0%	41.0%	25.0%
Boom	0.1	5.5%	45.0%	-21.0%	26.0%	38.0%

Answer 1

Expected return = sum of (probability*Return)
Expected return of T-Bills	(0.1*0.055)+(0.20*0.055)+(0.40*0.055)+(0.20*0.055)+(0.10*0.055)
Expected return of T-Bills	5.50%
T-bills are risk free asset and therefore there would be no risk and so standard deviation is 0
Expected return of HT	(0.1*(-0.27)) + (0.20*(-0.07))+(0.40*0.15)+(0.20*0.30)+(0.10*0.45)
Expected return of HT	12.40%
Calculation of standard deviation of HT
Economy	Probability	Return	(Return - Expected return)	(Return - Expected return)^2	Probability*((Return - Expected return)^2)
Recession	0.1	-27%	-39.40%	0.155236	0.0155236
Below Average	0.2	-7%	-19.40%	0.037636	0.0075272
Average	0.4	15%	2.60%	0.000676	0.0002704
Above average	0.2	30%	17.60%	0.030976	0.0061952
Boom	0.1	45%	32.60%	0.106276	0.0106276
				Variance	0.040144
				Standard deviation	20.04%
				(Variance^0.50)
Standard deviation of HT is 20.04%
Expected return of Coll	(0.1*(0.27)) + (0.20*(0.13))+(0.40*0)+(0.20*(-0.11))+(0.10*(-0.21))
Expected return of HT	1.00%
Calculation of standard deviation of HT
Economy	Probability	Return	(Return - Expected return)	(Return - Expected return)^2	Probability*((Return - Expected return)^2)
Recession	0.1	27%	26.00%	0.0676	0.00676
Below Average	0.2	13%	12.00%	0.0144	0.00288
Average	0.4	0%	-1.00%	0.0001	0.00004
Above average	0.2	-11%	-12.00%	0.0144	0.00288
Boom	0.1	-21%	-22.00%	0.0484	0.00484
				Variance	0.0174
				Standard deviation	13.19%
				(0.0174^0.50)
Standard deviation of Coll is 13.19%
Expected return of USR	(0.1*(0.06)) + (0.20*(-0.14))+(0.40*0.03)+(0.20*0.41)+(0.10*0.26)
Expected return of USR	9.80%
Calculation of standard deviation of USR
Economy	Probability	Return	(Return - Expected return)	(Return - Expected return)^2	Probability*((Return - Expected return)^2)
Recession	0.1	6%	-3.800%	0.001444	0.0001444
Below Average	0.2	-14%	-23.800%	0.056644	0.0113288
Average	0.4	3%	-6.800%	0.004624	0.0018496
Above average	0.2	41%	31.200%	0.097344	0.0194688
Boom	0.1	26%	16.200%	0.026244	0.0026244
				Variance	0.035416
				Standard deviation	18.82%
				(0.035416^0.50)
Standard deviation of USR is 18.82%
Expected return of MP	(0.1*(-0.17)) + (0.20*(-0.03))+(0.40*0.10)+(0.20*0.25)+(0.10*0.38)
Expected return of MP	10.50%
Calculation of standard deviation of MP
Economy	Probability	Return	(Return - Expected return)	(Return - Expected return)^2	Probability*((Return - Expected return)^2)
Recession	0.1	-17%	-27.500%	0.075625	0.0075625
Below Average	0.2	-3%	-13.500%	0.018225	0.003645
Average	0.4	10%	-0.500%	0.000025	0.00001
Above average	0.2	25%	14.500%	0.021025	0.004205
Boom	0.1	38%	27.500%	0.075625	0.0075625
				Variance	0.022985
				Standard deviation	15.16%
				(0.022985^0.50)
Standard deviation of MP is 15.16%