Question

Q2. A bank is considering two types of new investment options: Yield Bond (YB) and Equity Income (EI). Three possibilities are being considered: Yield Bond only; Equity Income only; and offering both YB and EI. Concerning the uncertainty about future demand, the bank management team estimates two potential demands for each type of investment: strong or weak, with the following probability assessments:

Equity Income Demand

Yield Bond Demand	Weak	Strong
Weak	0.15	0.45
Strong	0.25	0.15

The projected bank profit, in millions of dollars, has been also forecasted:

	Only Yield Bond	Only Equity Income
Weak	200	300
Strong	400	600

Both Yield Bond and Equity Income

Equity Income Demand

Yield Bond Demand	Weak	Strong
Weak	100	550
Strong	350	700

a) Determine the optimal strategy.

b) Determine the expected value of perfect information.

Answer 1

Let us assume we have 3 strategies such as

Yield Bond, Equity & Yield Bond-Equity Income both

We have Probability assesment given for both strategies in together hence need to find probabilities using bayesian probability

P(Yield Bond with Weak Demand | known demand for Equity Income)= 0.2/0.5 =0.4

P(Yield Bond with Strong Demand | known demand for Equity Income) = 1-P(Yield Bond with Weak Demand | known demand for Equity Income) = 0.6

Then Expected Income from Yield Bond

0.4(200)+0.6(400)=320

Expected income from Equity Income Demand

0.3/0.5=0.6 and 0.2/0.5 = 0.4 similarly usnig Bayesian probabilities

Expected income from Equity Income Demand

0.6(100)+0.4(600) =300

Now lets assume strategy when both are considered

weak,weak + weak,strong + strong,weak + strong,strong= 0.2(100)+0.3(300)+0.3(200)+0.2(700)=20+90+60+140=310

Hence given demand probabilities we can say that only equties would fetch better profits than that of others

To find Value of the constant B we need to have atleast expectedd value of strategy is 320

we need to have value B wich makes expected value of Equity Income-Yield bond atleast equal to 320

320= 20+90+60+0.2(B) that nakes B >=750
This is my solution..
Thank you