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Risk and Rate of Return
▪ Kathy Filgrade started Computer Products Corporation (CPC).
▪ Need more area to expand.
▪ Corporate with Randy Morely, who operates Morely Distributors
▪ Public their new company.
▪ T-bills: Short-term treasuries issued by US government
▪ T-bonds: Long-term treasuries issued by US government
▪ NASDAQ index: calculated by stocks listed on NASDAQ market
Table 1
Return on alternative investments
Estimated rates of return
Long-Run state of the economy
Prob.
T-bills
T-Bonds
CPC
MORELY
EAT
NASDAQ
Index
Recession
0.10
4.5%
10.0%
-18.00%
18.00%
-13.00%
-13.00%
Below avg.
0.20
4.5%
7.0%
-8.00%
14.0%
-6.0%
-2.0%
Average
0.40
4.5%
5.0%
11.00%
6.0%
10.0%
11.0%
Above avg.
0.20
4.5%
3.0%
26.00%
-1.0%
20.0%
17.0%
Boom
0.10
4.5%
2.0%
35.00%
-11.0%
30.0%
22.0%
expected return
4.50%
5.20%
9.70%
5.70%
8.50%
8.30%
Variance
0.0000
0.0005
0.02572
0.0066
0.0162
0.0103
std deviation
0.00%
2.23%
16.04%
8.11%
12.72%
10.17%
coef of var
0.0000
0.4283
1.6534
1.4232
1.4967
1.2252
0.00
-0.2178
1.5562
-0.7608
1.2299
1.0000
Beta coefficient
▪ CPC has the highest expected return with the highest risk.
▪ T-bills is the most stable investment with lowest return.
▪ NASDAQ index means market rate, has the similar occasion with regional
restaurant EAT
▪ Morely is a little lower than others, expect T-bills and T-bonds.
▪ SML Equation: k=kern+(kM-kRF)b.
▪ 40% CPC 60%EAT
▪ 50%CPC 50%Morely
▪ 50%Morely 50%EAT
Table 2
Returns on Portfolios
Portfolio
Long-Run state of the economy
Prob.
50% CPC 50%
Morely
40% CPC 60%
EAT
50% Morely 50%
EAT
Recession
0.10
0.00%
-15.00%
2.50%
Below avg.
0.20
3.00%
-6.80%
4.00%
Average
0.40
8.50%
10.40%
8.00%
Above avg.
0.20
12.50%
22.40%
9.50%
Boom
0.10
12.00%
32.00%
9.50%
expected return
7.70%
8.98%
7.10%
Variance
0.0017
0.0197
0.0006
std deviation
4.13%
14.04%
2.47%
coef of var
0.5364
1.5635
0.3476
Beta coefficient
0.3997
1.3602
0.2388
SML Eq.
Exp Rate
CPC =
9.94%
9.70%
Morely =
2.81%
5.70%
EAT =
8.98%
8.50%
▪ Undiversifiable risk, systematic risk,
market risk
▪ Caused by inflation, interest rate
change, or politic instability
▪ Diversifiable risk
▪ Caused by the certain company or
industry
▪ Project can be financed with internal funds.
▪ Project is very large and securities must be sold to finance it.
▪ Project is very long and will take years to complete.
▪ Investment is short-term and the company will receive the cash flows within few
months.
▪ Well-diversified portfolio can reduce the risk.
▪ Combination between CPC and Morely is more reasonable.
Filmore Enterprises Risk and Rates of Returns
Case #84
Page 1
Abstract
Kathy Filgrade is the owner and founder of Computer Products Corporation. At CPC, Kathy
designs custom and unique computer systems for her clients. Kathy has expanded to operate six
“mega stores”. Kathy wants to explore the options of expanding CPC and incorporate a cybercafé. During this exploration, she has partnered with Randy Morely, owner and founder of
Morely Distributors. Together they want to combine their business knowledge, use their
connections and create Filmore Enterprises. However, because both Kathy and Randy have most
of their finances secured within other business, they have requested analysts to prepare a
discussion on the risk and return issues that come along with their new business venture, Filmore
Enterprises. Throughout this write up, we will address the major risk and return concerns that
Kathy and Randy need analyzed.
Case #84
Page 2
Expected Rate of Return
Kathy and Randy need to evaluate the expected rate of return. Refer to Table 1. If you
focus in on expected rate of return only, CPC has the highest return out of all the investments,
and appears to be the best investment. On the other hand, T-Bills have the lowest expected return
for the investments, resulting in the worst investment.
When you evaluate CPC, and EAT investments, you find that the state of the economy
must be average or above for there to be a positive return on investment. If the economy is below
average, then CPC and EAT investments have negative returns. This makes CPC and EAT to be
more risky investments; however, CPC appears to have the most risk involved. This is because
CPC loses the most during an economy recession, and it gains the most during economy boom.
Morely is the complete opposite. Morely produces negative return on investments when
there is a boom in the economy. When there is an economy recession, Morely produces positive
investments.
Kathy and Randy need to know the expected rate of return for each investment so they
understand which investment will be more profitable for their business plans.
Long-Run State of
the Economy
Recession
Below Average
Average
Above Average
Boom
Expected Return
Case #84
Returns on Alternative Investments
Estimated Rates of Return
Prob. TTCPC
Morely EAT
NASDAQ
Bills
Bonds
Index
0.10 4.50% 10.00%
– 18.00%
-13.00%
18.00%
13.00%
0.20 4.50%
7.00% -8.00% 14.00% -6.00%
-2.00%
0.40 4.50%
5.00% 11.00%
6.00% 10.00%
11.00%
0.20 4.50%
3.00% 26.00% -1.00% 20.00%
17.00%
0.10 4.50%
2.00% 35.00%
– 30.00%
22.00%
11.00%
4.50%
5.20%
9.70%
5.70%
8.50%
8.30%
Page 3
US Treasuries and the US Government: T-Bills, T-Bonds, & Bond Ratings
Please Refer the above Table. Notice that no matter the state of the economy, the T-Bill
remains at 4.5 percent. This is because the 4.5 percent is not affected by the state of the
economy, unlike the other investments. The US Treasury is responsible for redeeming the TBills at par regardless of the economy’s current state. This makes the T-Bills risk-free in the
default risk sense. 4.5 percent will be redeemed no matter what state of the economy.
However, T-Bills are made up of two components, the real risk-free rate plus an
additional inflation premium. This is the catch that Kathy and Randy must be aware of. Inflation
is always uncertain. Because of this, it is highly unlikely that the realized real rate of return
would equal the expected 4.5 percent. This shows that T-Bills are not completely risk free. In
terms of purchasing power, there are some risks to these investments.
T-Bills are also exposed to reinvestment rate risk. If Kathy and Randy invested in a TBill portfolio, and after the investment the rates declined, then their nominal income would fall
due to the reinvestment rate risk. This tells us that the US does not have any true risk free
securities. If the treasury sold inflation-indexed, tax-exempt bonds, they would be truly riskless,
but all actual securities are exposed to some type of risk.
On the other hand, T-Bond’s investment returns vary. This is due to T-Bonds rates being
inversely correlated with the market. A good example of this would be that if the economy is in
recession, the demand for T-Bonds increase ultimately causing the rates to increase. The lower
the current market, the less risks, the more fixed rates, and the higher demand for T-Bonds.
The corporate bonds that Filmore enterprise might issue carries a higher default risk than
T-bonds because they are not back by the US government. Because of the potential higher risks,
it would be dependent on potential bond ratings for Filmore Enterprises since bond ratings affect
Case #84
Page 4
the cost of borrowing. More creditworthy bond issuers borrow at lower costs, where less
creditworthy have higher interest. This means that bonds with higher credit almost always carry
the lowest yields. It would be essential for Kathy and Randy to evaluate the bond ratings.
Using Standard Deviation and Coefficient of Variation to Show Risk and Return Tradeoff
Basing a decision solely on expected returns is appropriate only for risk-neutral
individuals. Since most people are risk averse, risk is an important consideration for the decision.
Two possible measures of risk are the standard deviation and the coefficient of variation. See
Table below showing the standard deviation and coefficient of variation for each investment.
Standard Deviation and Coefficient of Variation
TBills
Expected
Return
Variance
Standard
deviation
Coefficient of
Var (CV)
TBonds
Morely EAT
CPC
4.50%
5.20%
0
0.00%
5 257.21
2.23% 16.04%
0
0.43
9.70%
1.65
5.70%
NASDAQ
Index
8.50%
8.30%
65.8
161.9
8.11% 12.72%
103.4
10.17%
1.42
1.5
1.23
Typically, the higher the risk on investment, the higher the return on invest is expected to
be. Per the above table, CPC exemplifies the highest standard deviation, coefficient of variation,
but it also has the highest expected return. Morely is unusual because it only has slight returns
during the average state resulting in this investment being a higher coefficient of variation. With
Morely having the higher CV, it shows that is has more return than NASDAQ.
If investors created a 2-stock portfolio by investing $100,000 in CPC and $100,000 in
Morely the expected return for each state of the economy, and the expected return for the
portfolio would show changes.
Case #84
Page 5
Long-Run State of
the Economy
Recession
Below Averag
Average
Above Average
Boom
Returns on Portfolios
Portfolio
Prob.
50%CPC
40%CPC
50%
60% EAT
Morely
0.10
0.00%
-15.00%
0.20
3.00%
-6.80%
0.40
8.50%
10.40%
0.20
12.50%
22.40%
0.10
12.00%
32.00%
50% Morely
50%EAT
Expected Return
Variance
7.70%
17.06
8.98%
Std deviation
Coefficient of Var
(CV)
197.10
6.10
4.13%
14.04%
0.54
1.56
0.35
2.50%
4.00%
8.00%
9.50%
9.50%
7.10%
2.47%
By looking above, we see that the individual stocks have a lower SD than the portfolio
does. This shows diversification within the investments, and shows that it’s lowered the risks for
the portfolio.
If you look at EAT and CPC as a portfolio, it shows that the SD is higher. This indicates
that there is less diversification due to the fact each business is highly correlated. Morely has a
high positive return during recession, so when combined with CPC which provides high returns
in boom it provides great diversification. The Morely and CPC combo have a highly negatively
correlated relationship, which ultimately provides lower risk than the other portfolio. This is
shown through the lower SD.
The Changes in Risk as Investors Add More Randomly-Selected Stocks to the Portfolio
As investors add more and more randomly selected stocks to the portfolio, risk will be
diversified and standard deviation from the mean will decrease. Some of the stocks yield high
rate of return considering higher the risk and higher the standard deviation, some of the stocks
yield low rate of return considering the low risk and lower the standard deviation.
Case #84
Page 6
Similarly, some of the stocks yield high return, or higher standard deviations, on one time
of economy, and some of the stocks yield low rate, or lower standard deviations, on similar
economy.
For example, in table 1 and 2 on the case file. If we consider table 1, if investors invest all
their stock on CPC only, then their standard deviation will be 16.04, and if they invest all in
Morely, then standard deviation will be 8.11. But review table 2 from the case file. If they
diversified their investment both in CPC and Morely (50%) each, then standard deviation will be
4.13, that mean risk will be diversified.
As portfolio increases, standard deviation will be decreases as a lessor margin than before
at certain extend. But, after that no matter how much investors diversified the investment to the
portfolio, standard deviation will not decrease; this is mainly due to non-diversified risk such as
inflation.
Portfolio standard Deviation
30.00%
25.00%
20.00%
15.00%
Portfolio standard Deviation
10.00%
5.00%
0.00%
1
2
3
4
5
6
7
8
In following above example, x axis represent number of shares on portfolio, and the y
axis represents portfolio standard deviation. As Kathy and Randy increase the number of shares
Case #84
Page 7
on portfolio, from 1 to 2, the standard deviation decreases significantly, so as reduces the risk
significantly. Similarly, from 2 to 3, standard deviation decreases, but at a lesser degree as
compare to from 1 to 2. At point, when number of stocks reached to 6 or more, standard
deviation will not be decrease due to non-diversifiable risk.
What implication does diversification have to investors?
Diversification Strategy can help Investor to achieve more consistent returns over time
and help to reduce overall investment Risk. Diversification makes investor more secured in
investment. For example, some of the investment can get better return on economic boom and
some of the investment can give better return on depression. Holding stocks on both investments
will make investor more secured; one’s return will be offset by others.
If an investor decides to hold a 1 stock portfolio and a result is exposed to more risk than
diversified investors, Non-diversified investor expect to be compensated for all his or her risk.
Market risk premium and beta factor defines play a vital role to defined his expected return. For
example, if Risk free rate is 5%, Market risk premium is 9% and the beta factor is 2 then, his
expected return should be 23%. On this case his expected return will be more than others (risk
free rate + market risk premium) as he invests twice riskier (systematic) investment.
The Difference between Total Risk, Diversifiable Risk and Market Risk
Total risk is the sum of systematic risk (market risk) and unsystematic risk (diversifiable
risk). Systematic risk also called as market risk, cannot be eliminated through diversification but
unsystematic risk can be eliminated by diversification. Total risk is also measured by standard
deviation of return.
Case #84
Page 8
Portfolio standard Deviation
30.00%
25.00%
Diversifiable risk
20.00%
15.00%
Portfolio standard Deviation
10.00%
Non-diversifiable
risk(Market risk)
5.00%
0.00%
1
2
3
4
5
6
7
8
At indicated on arrow point, where standard deviation of non-diversifiable risk is 14% and
standard deviation of diversifiable risk is 6%, so the total risk is 20%.
Desire of diversification bases on various factors, such as age of persons, type of
organization, and place of organization that involved in retirement fund. When people get closer
to retirement, their desire normally is to invest his portion of retirement fund on secured
investment such as Treasury Bills and T Bonds. Similarly, normally in the people are young and
lot of time to retire then, they want their money to invest on stocks, so they will get more return
as compared to Treasury bills and Treasury Bonds as bearing the more risk. Desire of
diversification is also based on markets economy and type of portfolio. Some portfolio will give
better return in average economy and some will give comparatively low return on average
economy.
See chart below. The characteristics for CPC, Morely, and T-Bills are plotted, showing
the returns on the market on the x-axis and returns on the asset on the y-axis.
Case #84
Page 9
(Characteristics Line – CPC, Morely, T Bills with N. Index)
Slope of line for T-bills and NASDAQ is zero. Slope of CPC and NASDAQ is 1.5 (positively
correlated). Slope of Morely with NASDAQ is -0.77 (Negatively correlated)
Year
T Bills NASDAQ slope
CPC
NASDAQ slope
Morely NASDAQ slope
1
4.5
-13
0
-18
-13 1.534063
18
-13
0.77494
2
4.5
-2
-8
-2
14
-2
3
4.5
11
11
11
6
11
4
4.5
17
26
17
-1
17
5
4.5
22
35
22
-11
22
The slope coefficient is almost same as Table 1.
The distance between the plot points and the regression line is the fluctuation of the return on
stocks on market trend. Sometimes it yields better than market sometimes it yields less than
market. This distance is representing as Variance from the linear trend. This distance is called as
Case #84
Page 10
residuals. It is Positive if it’s above line and negative if it’s below linear trend. Above line
indicate the return more than linear trend, similarly it its below trend then, residual should be
negative.
Beta is relative measure for stock on the market. 1 consider at market risk. If Beta is more
than 1 of stock mean more risk than the market trend. If beta is less than 1 then, risk is less on
that as compared to other on that market. In table 1, NASDAQ symbol as Market. Beta
coefficient on CPC is 1.53 and EAT is 1.22, that mean return on CPC is riskier than EAT.
It looks like relevant relative to the marker. CPC has the highest risk and has highest
expected rate of return as compared to others. Looks relative to the market i.e. higher the beta,
higher the expected rate of return.
Beta & Expected Return
12
10
8
6
Expected retrun
4
Beta Coefficient
1.53
2
1.22
1
0
0
T Bills
-2
Tbonds
-0.22
CPC
Morely
-0.77
EAT
NASDAQ
The Security Market Line
If T-bonds serve as the risk-free rate and NASDAQ index as the market, then the
following equation serves as the slope of the SML:
Case #84
Page 11
Slope = E(Rm) – Rf = market risk premium => Slope = 8.3% – 5.2% = 3.1. This means y = 3.1x
+ 5.2% is the equation of the SML. The graph below reflects our calculation. Notice that when
Beta is equal to zero, the Y-intercept is at our T-bond risk-free rate of 5.2%. The SML represents
the reward for bearing an average amount of systematic risk.
Required Rate of Return Based on SML vs Expected Rate of Return
The capital asset pricing model (CAPM) can help us find the required rate of return for
our portfolio. The equation, CAPM, can be written as: E(Ri) = Rf + Bi [E(Rm) – Rf]. So,
CPC’s required rate of return = 5.2% + 1.53 [8.3% – 5.2%] = 9.94%
Morely’s required rate of return = 5.2% + (-.077) [8.3% – 5.2%] = 2.81%
EAT’s required rate of return = 5.2% + 1.33 [8.3% – 5.2%] = 8.98%
If we take a look at our calculations in expected returns of our financial assets listed in Table 1, it
is easy to compare and conclude whether to buy or sell each stock given the conditions.
Case #84
Page 12
Long-Run State of
the Economy
Recession
Below Average
Average
Above Average
Boom
Expected Return
Returns on Alternative Investments
Estimated Rates of Return
Prob. TTCPC
Morely EAT
NASDAQ
Bills
Bonds
Index
0.10 4.50% 10.00%
– 18.00%
-13.00%
18.00%
13.00%
0.20 4.50%
7.00% -8.00% 14.00% -6.00%
-2.00%
0.40 4.50%
5.00% 11.00%
6.00% 10.00%
11.00%
0.20 4.50%
3.00% 26.00% -1.00% 20.00%
17.00%
0.10 4.50%
2.00% 35.00%
– 30.00%
22.00%
11.00%
4.50%
5.20%
9.70%
5.70%
8.50%
8.30%
CPC’s expected return is lower than its required return; therefore the stock is overvalued
and should be sold. The same can be said for EAT. For Morely, though, the expected return is
higher than required return. This stock is undervalued and should be bought.
The stocks are not in equilibrium. To restore equilibrium, the stocks below the line would
have to either lower the level of risk in relation to the market or increase the expected return of
that stock to match the required return. For a stock above the line, equilibrium would be restored
by decreasing the return to the market’s level of return or the risk would need to increase to
match its point on the SML. For stocks, this is determined by the business activities of the
corporation it represents. Investors look to take advantage of stocks that will produce higher
returns than the required return based on the SML. These forces contribute to establishing a
stock’s equilibrium in the market. A stock may also be underpriced or overpriced in the market,
but trading on the open market will generally move the stock back to its true value in the market,
or equilibrium.
Beta coefficient for a 40/60 portfolio of CPC-EAT and The Required Rate of Return
The Beta for this portfolio can be calculated as such: Bp = 0.40 x Bcpc + 0.60 x Beta
Case #84
Page 13
Bp = 0.40 x 1.22 + 0.60 x 1.53 = 1.41, the beta for a 40/60 portfolio of CPC-EAT.
Continuing, we can calculate the required rate of return to be 26 …
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