Question

Alpha is deciding whether to invest $1 million in a project. There is a 70% chance that the project will be successful, yielding a return of 20% on investment. However, there is a 30% chance that the project will fail, in which case Alpha will only recover 80% of his investment.

1. What is the expected value of investing in the project?

2. Suppose Alpha evaluates the project in accordance with prospect theory. Specifi- cally,

v(x) = (x − r)^0.8 .if x ≥ r

−λ(r − x)^0.8 ,if r > x,

where λ > 1, r = $1 million is the reference point, and x is the amount of money received by Alpha at the end of the project. The corresponding probability weighting functions are such that γ = δ = 0.6.

(a) Argue (mathematically) that Alpha is loss averse.

(b) What is Alpha’s value of investing in the project if λ = 2?

(c) Find the value of λ such that Alpha is indifferent between investing and not investing in the project.

Beta’s boss assigns him a task on Monday which must be completed before Wednesday. The task takes a total of 10 hours. If Beta works on the task for Xt hours on day t, then he suffers a disutility of Xt^2 on day t. Throughout the problem t ∈ {1, 2, 3}, where 1 stands for Monday, 2 for Tuesday, and 3 for Wednesday. Beta’s time preferences are given by exponential discounting with the discount factor of δ = 0.8 per day.

1. What is the present value (as measured on Monday) of Beta’s disutility if he works for 6 hours on Monday and 4 hours on Tuesday?

2. Beta’s problem is to complete the task before Wednesday in such a way to minimize the present value of his distuility (as measured on Monday). Write down the mathematical version of Beta’s problem (that is, minimize some function subject to some constraint)

3. How many hours does Beta choose to work the task on Monday?

4. Now suppose that the boss wants to assign a new task to Beta on Tuesday and would therefore like Beta to have more time on Tuesday. She incentivizes Beta by offering him a reward of r3 = 10x1 on Wednesday if Beta works on Monday for x1 hours on the first task. How many hours does Beta choose to work on Monday?

Answer 1

1.Expected value of project is as under

= 1Million $ success rate is 70%

0.7 million @ 20% addition = 0.14

Total Accural = 1 million $ +0.14 million $ =1.14 Million Dollar

Lost cost = 1 Million $ convert due to loss of 20% which is 30% chance that is = 0.3 @ 20% = 0.6% decrease

1.14-0.6=1.08 Million Dolloar

expected value is = 0.8 million dollar profit +1.00 million $ =total 1.08 Answer

2 (A)

.My aruge that alpha is loss averse

Alpha is always due to fund manager / controller risk that occurs is

suppose risk appatite is <0.5 but due to alpha it comes >0.5 it means

alpha is generating more risk on project which is mathematically is = 0.8,0.7,0.6.....>0.5 Answer

(B) Alpha value of investing is = suppose if we assume down y is = 1.5 which is more < 2

but contrains 0.6 so alpha value of investing is 1.5+0.6-2=0.1(Favourable) Answer....

(C) if round y is = 2 in investing it occur 20% addition but not investing it decrease 0.14-0.6

if investing then favourable ration net 1.8 i.e +0.2,

not investing loss due opportunity cost 2.00-0.6 =1.4 negative Answer

1. PV is 6 hours =1.20 -(0.60%)less i.e. 0.48

PV is 4 hours = 1.20- (0.40%)less i.e. 0.80

2. Beta in mathematical form due to >1 Answer

3.To reduce beta on Monday time is avg. of 0.60+0.4=0.5 hours Answser

4. To choose work on Monday is less then 0.5 hours to desired level answer