Question
In: Finance
a financial analyst you are trying to put together a report about three different bonds. One...
a financial analyst you are trying to put together a report about three different bonds. One portion of the report requires you to estimate the expected return and standard deviation of each bond.
Which bond has the highest expected return?
Which bond has the riskiest? [Hint: You must use the probability model to compute the expected risk]
|
Probability |
Yield for Bond X |
Yield for Bond Y |
Yield for Bond Z |
|
0.10 |
12% |
14% |
7% |
|
0.20 |
4% |
3% |
9% |
|
0.30 |
23% |
7% |
15% |
|
0.05 |
6% |
-20% |
30% |
|
0.15 |
8% |
5% |
2% |
|
0.09 |
1% |
-12% |
0.1% |
|
0.11 |
9% |
2% |
10% |
In excel. How do you know which bond is risker than the other?
Solutions
Expert Solution
a) Calculation of expected return of each bond.
| Probability (P) | Yield for Bond X in % (X) | Yield for Bond Y in % (Y) | Yield for Bond Z in % (Z) | P*X | P*Y | P*Z |
| 0.10 | 12 | 14 | 7 | 1.20 | 1.40 | 0.70 |
| 0.20 | 4 | 3 | 9 | 0.80 | 0.60 | 1.80 |
| 0.30 | 23 | 7 | 15 | 6.90 | 2.10 | 4.50 |
| 0.05 | 6 | -20 | 30 | 0.30 | -1.00 | 1.50 |
| 0.15 | 8 | 5 | 2 | 1.20 | 0.75 | 0.30 |
| 0.09 | 1 | -12 | 0.1 | 0.09 | -1.08 | 0.01 |
| 0.11 | 9 | 2 | 10 | 0.99 | 0.22 | 1.10 |
Expected Return on Bond X = 
P*X
= 1.2+.8+6.9+.3+1.2+.09+.99
= 11.48%
Expected Return on Bond Y =
P*Y
= 1.40+.6+2.1-1+.75-1.08+.22
= 2.99%
Expected Return on Bond Z =
P*Z
= .7+1.8+4.5+1.5+.3+.01+1.1
= 9.91%
Bond X has higher expected return.
b) Calculation of standard deviation of each bond.
-BOND X
| Probability (P) | Yield for Bond X in % (X) | Deviation from expected return of 11.48% (D) | PD2 |
| 0.10 | 12 | 0.52 | 0.0270 |
| 0.20 | 4 | -7.48 | 11.1901 |
| 0.30 | 23 | 11.52 | 39.8131 |
| 0.05 | 6 | -5.48 | 1.5015 |
| 0.15 | 8 | -3.48 | 1.8166 |
| 0.09 | 1 | -10.48 | 9.8847 |
| 0.11 | 9 | -2.48 | 0.6765 |
Variance =
PD2
= 64.9096
Standard Deviation =
Variance
=
64.9096
= 8.06%
-BOND Y
| Probability (P) | Yield for Bond Y in % (Y) | Deviation from expected return of 2.99% (D) | PD2 |
| 0.10 | 14 | 11.01 | 12.1220 |
| 0.20 | 3 | 0.01 | 0.0000 |
| 0.30 | 7 | 4.01 | 4.8240 |
| 0.05 | -20 | -22.99 | 26.4270 |
| 0.15 | 5 | 2.01 | 0.6060 |
| 0.09 | -12 | -14.99 | 20.2230 |
| 0.11 | 2 | -0.99 | 0.1078 |
Variance =
PD2
= 64.3099
Standard Deviation =
Variance
=
64.3099
= 8.02%
-BOND Z
| Probability (P) | Yield for Bond Z in % (Z) | Deviation from expected return of 9.91% (D) | PD2 |
| 0.10 | 7 | -2.91 | 0.8468 |
| 0.20 | 9 | -0.91 | 0.1656 |
| 0.30 | 15 | 5.09 | 7.7724 |
| 0.05 | 30 | 20.09 | 20.1804 |
| 0.15 | 2 | -7.91 | 9.3852 |
| 0.09 | 0.1 | -9.81 | 8.6612 |
| 0.11 | 10 | 0.09 | 0.0009 |
Variance =
PD2
= 47.0126
Standard Deviation =
Variance
=
47.0126
= 6.86%
Bond X is riskiest since it has higher standard deviation.
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