The T-bills return is Independent of the state of economy because it is a risk free rate guaranteed by the government. They are risk free as long as country is not being questioned.
2. Altas is to supple protective equipments to construction workers. When the economy is doing good demand is more and when economy is bad demand is low. Repo Mens is to provide bio-mechanic organs to people who are in need and is independent of the status of the economy. It will not be affected is economy is good or bad.
C. Alta Industries Expected Return
E(R) = .10(-.22)+.20(-.02)+.4(.2)+.2(.35)+.1(.5) = 12.4+5
E(R) = 17.4%
Repo Men Expected Reture
E(R)) = .10(.03)+.40(.10)+.10(.15) = .058 = E (R) = 5.8%
D. 1.
State of economy
|
Probability
|
Returen(2)
|
(E ) R)(3)
|
Deviation (2-3)=4
|
Squared Deviation 4^2
|
Squared Deviation x Probability=5
|
Recession
|
0.1 |
-0.22 |
-0.022 |
0.242 |
0.058 |
0.1 |
Below Average
|
0.2 |
-0.02 |
-0.004 |
-0.016 |
0.00025 |
0.2 |
Average
|
0.4 |
0.2 |
0.08 |
0.12 |
0.0144 |
0.4 |
Above Average
|
0.2 |
0.35 |
0.07 |
0.28 |
0.0784 |
0.2 |
Boom
|
0.1 |
0.5 |
0.05 .174 |
0.45 |
.2025 .04786 |
0.1 |
Squared Root of Squared Deviation X Probability = Squared Root of .04786
=.21 or 21%
State of economy
|
Probability
|
Returen(2)
|
(E ) R)(3)
|
Deviation (2-3)=4
|
Squared Deviation 4^2
|
Squared Deviation x Probability=5
|
Recession
|
0.1 |
0.03 |
0.003 |
0.027 |
0.0007 |
0.1 |
Average
|
0.4 |
0.1 |
0.04 |
0.06 |
0.0036 |
0.4 |
Boom
|
0.1 |
0.15 |
0.015 |
0.018 |
0.1 |
0.058 |
0.087 |
0.0223 |
|
Square root of the Squared Deviation X Probability = squared root of .0223
=.149
2. Standard Deviation measures the total risk associated with a securities return. The expected return on the security is measured.
3.
E. Here is the Calculation of the Coefficient of variation (CV)
CV=.174/.21 = .82
Here is the Calculation of Coefficient of Variables for 2 stock portfolios
.058/.057
CV = 1.01
No the same risk ranking of Standard Deviation is not produced.
F. A 2 stock portfolio of Alta and Repo ($50K each)
E ( R ) = .50(.174) + .5(.017)
= .087 + .0085
= E ( R ) = .0955
2. Calculation of SD
E ( R )
|
R - E ( R )
|
R - E ( R ) ^2
|
Wt
|
Squared Deviation Probability = 5
|
0.087 |
-0.0085 |
0.00007 |
0.5 |
0.000035 |
0.0085 |
-0.0087 |
0.00007 |
0.5 |
0.000035 |
0.0955 |
0.00007 |
Squared Deviation X Probability = Squared root of .00007
= .008
CV = .0955/.008 = CV = 11.90
The CV of Alta with 17.4% is more than the portfolio variation of 11.9%. The CV of Repo with 7.9% is more than 11.9% of the 2 stock.
I. Market risk for individual securities is measured by BETA, a measure of systematic risk. Beta Co-efficient is calculated by taking Standard Deviation of stock I divided by Standard Deviation of the market returns.. Then taking that number times Correlation between I and M
J.
Years
|
Market (%)
|
PQU (%)
|
1 |
25.7 |
40 |
2 |
8 |
-15 |
3 |
-11 |
-15 |
4 |
15 |
35 |
5 |
32.5 |
10 |
6 |
13.7 |
30 |
7 |
40 |
42 |
8 |
10 |
-10 |
9 |
-10.8 |
-25 |
10 |
-13.1 |
25 |
Beta = .396
For every 1% of change in the market return the stocks return change is .396.
K.
Security
|
Return
|
Risk (Beta)
|
Alta |
17.4 |
1.29 |
Market |
15 |
1 |
American Foam |
13.8 |
0.68 |
T-bills |
8 |
0 |
Repo Men |
1.7 |
-0.86 |
- The returns on the securities are related to the market risk of individual securities.
- Based on the beta, stocks can be selected. There is a relation between return and risk if you look at the table used.