Question

Imagine a given capital market where a risk-free asset with a return, rf, of 6% per period is traded. On the given capital market, the only assets traded, besides the risk-free, are stocks in firm A, firm B and firm C. Thus, no other risky assets are traded on the capital market. The price today (t = 0) of a stock in A is DKK 50. On the capital market, all participants agree that in one period (to time t = 1) there are only 4 possible states for the value of stock A, cf. table 2.1 below:

State	Probability	Price at t= 1 in firm A
1	0,15	47,00
2	0,15	44,50
3	0,30	43,50
4	0,40	45,00

No matter which state is realized, a dividend of DKK 10 per stock in firm A is paid in the next period (after t = 0 and before t = 1). The realized return of stock B in the next period, for the states, is given in table 2.2 below:

State	Realized return of stock B in next period
1	-0,0700
2	0,1300
3	0,1500
4	0,0800

Calculate the expected return and the variance of the return in the next period, for firm A and B.

Answer 1

Realized return(R_e) =

(P1 - Po) +D Po

Expected return =

5 P*R

Standard Deviation =

ΙΣ(R, – R.)2 και P,

Variance =

Σ(R, – R.)? και Ρ:

State	Probability	Firm A							Firm B
		Price (P2)	Dividend	Relized return(R)	P*R	(R-Re)^2	P*(R-Re)^2		Relized return(R)	P*R	(R-Re)^2	P*(R-Re)^2
1	0.15	47	10	14.00%	0.021	0.198%	0.030%		-7.00%	-0.0105	2.434%	0.365%
2	0.15	44.5	10	9.00%	0.0135	0.003%	0.000%		13.00%	0.0195	0.194%	0.029%
3	0.3	43.5	10	7.00%	0.021	0.065%	0.020%		15.00%	0.045	0.410%	0.123%
4	0.4	45	10	10.00%	0.04	0.002%	0.001%		8.00%	0.032	0.004%	0.001%
						Variance	0.050%	Sum			Variance	0.518%	Sum
				Expected return(Re)	9.55%	Standard deviation	2.247%	0.05%^0.5	Expected return(Re)	8.60%	Standard deviation	7.200%	0.518%^0.5
					Sum of above					Sum of above