Actual return |
Expected return= Probability* actual return |
||||
state |
probability |
A |
B |
A |
B |
strong boom |
0.15 |
-0.60 |
0.75 |
-0.0900 |
0.1125 |
weak boom |
0.20 |
-0.30 |
0.50 |
-0.0600 |
0.1000 |
average |
0.05 |
-0.10 |
0.15 |
-0.0050 |
0.0075 |
weak recession |
0.40 |
0.20 |
-0.10 |
0.0800 |
-0.0400 |
strong recession |
0.20 |
0.80 |
-0.35 |
0.1600 |
-0.0700 |
Total |
0.0850 |
0.1100 |
For strong boom , A: expected return = 0.15*-0.06, weak boom = 0.20*-0.30 and so on.
For strong boom ,B: expected return = 0.15*0.75, weak boom = 0.20*0.50 and so on.
So the return for A= 8.50 %
And B= 11.00%
Standard deviation = [( actual return-expected return)2* ( probability)]1/2
Actual return |
Expected return |
S= (Given return - expected return) ^2 |
D= S*P |
||||||
state |
probability |
A |
B |
A |
B |
A |
B |
A |
B |
strong boom |
0.15 |
-0.60 |
0.75 |
0.0850 |
0.11 |
0.4692 |
0.4096 |
0.0704 |
0.0614 |
weak boom |
0.20 |
-0.30 |
0.50 |
0.1482 |
0.1521 |
0.0296 |
0.0304 |
||
average |
0.05 |
-0.10 |
0.15 |
0.0342 |
0.0016 |
0.0017 |
0.0001 |
||
weak recession |
0.40 |
0.20 |
-0.10 |
0.0132 |
0.0441 |
0.0053 |
0.0176 |
||
strong recession |
0.20 |
0.80 |
-0.35 |
0.5112 |
0.2116 |
0.1022 |
0.0423 |
||
Total |
0.0850 |
0.1100 |
0.2093 |
0.1519 |
Standard deviation = D^1/2 |
|
A: |
=(0.2093)^1/2 |
=0.4575 |
|
B: |
=(0.1519)^1/2 |
= 0.3897 |
Here, for strong boom , in A: S= (-0.60-0.085))^2
Weak boom = (-0.30-0.085)^2
And so on
Similarly for B:
for strong boom , in B: S= (0.75-0.11))^2
Weak boom = (0.50-0.11)^2
And so on
And for D: for A:
Strong boom= 0.15*0.4692
Weak boom = 0.20*0.1482
And so on.
coefficient of variation (COV)= standard deviation/ expected return rate
for A:
SD= 0.4575
Expected return = 8.50%
COV= 0.4575/0.085
= 5.38
for B:
SD= 0.3897
Expected return = 11%
COV= 0.3897/0.11
=3.54
Actual return |
Expected return |
V= (Given return - expected return) |
C= P* (V of A)*(V of B) |
|||||
state |
probability |
A |
B |
A |
B |
A |
B |
|
strong boom |
0.15 |
-0.60 |
0.75 |
0.0850 |
0.11 |
-0.69 |
0.64 |
-0.0658 |
weak boom |
0.20 |
-0.30 |
0.50 |
0.0850 |
0.11 |
-0.39 |
0.39 |
-0.0300 |
average |
0.05 |
-0.10 |
0.15 |
0.0850 |
0.11 |
-0.19 |
0.04 |
-0.0004 |
weak recession |
0.40 |
0.20 |
-0.10 |
0.0850 |
0.11 |
0.12 |
-0.21 |
-0.0097 |
strong recession |
0.20 |
0.80 |
-0.35 |
0.0850 |
0.11 |
0.72 |
-0.46 |
-0.0658 |
Total sum |
-0.1716 |
So the C for strong boom will be = 0.15*-0.69*0.64= -0.065
Weak boom = 0.20*-0.39*0.39=-0.03
And so on
So Covariance= -0.1716
= -0.1716/(0.4575*0.3897)
= -0.9625
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