You are confronted with the opportunity to participate in a project with the fol
ID: 2753097 • Letter: Y
Question
You are confronted with the opportunity to participate in a project with the following known distribution of returns:
State
Prob
Project ROR
1
1/4
20%
2
1/2
15%
3
1/4
-4%
A bank will allow you to borrow -- at 8% -- up to the amount of your own money that you commit to the project (i.e., if you invest, say $10 of your own money, you can borrow another $10 to do the same).
a.) What will be the standard deviation of the ROR you will earn if you borrow the maximum amount?
b.) You decide to invest $100 of your own funds and invest another $100 more of borrowed funds. What will be your wealth position at the project's close if state 3 occurs?
State
Prob
Project ROR
1
1/4
20%
2
1/2
15%
3
1/4
-4%
Explanation / Answer
State
Prob
ROR
Mean
X-X1
(X-X1)^2
1
0.25
20%
5.00%
-6.50%
0.0042
2
0.50
15%
7.50%
-4.00%
0.0016
3
0.25
-4%
-1.00%
-12.50%
0.0156
11.50%
0.0215
Standard deviation = sqroot(0.0215) = 0.1465
b)if State 3 occurs,
Return = 100+100+100*-4%*0.25-100*8%
=200-1-8 = 191
State
Prob
ROR
Mean
X-X1
(X-X1)^2
1
0.25
20%
5.00%
-6.50%
0.0042
2
0.50
15%
7.50%
-4.00%
0.0016
3
0.25
-4%
-1.00%
-12.50%
0.0156
11.50%
0.0215
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