# Financial Management

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Financial Management ­ MGT201
VU
Lesson 20
RISK FOR A SINGLE STOCK INVESTMENT, PROBABILITY GRAPHS AND CO-
EFFICIENT OF VARIATION
Learning Objectives:
After going through this lecture, you would be able to have an understanding of the following
topics
·  Risk for Single Stock Investment
·  Probability Graphs and Coefficient of variation
In this lecture, we will continue our discussion on risk and return. This is very important area of
financial management.
In previous lecture, we have mentioned an example for the investment in share and after one
year the share price has 3 possible outcomes. This uncertainty in future price of the share that leads to
the certain distribution in forecasted share price and this distribution is source of the uncertainty which
allow us to calculate risk.
3 Possible Outcomes Example Continued:
Measuring Stand Alone Risk for Single Stock Investment
Std Dev = δ =
√ ∑ (r i - < r i >) 2 p i.
=
((r i - < r i >) 2 p i.)) 0.5.
=  {[(40-10)2 (0.3)] + [(10-10)2 (0.4)] + [(-20-10)2 (0.3)] } 0.5 .
=  {270 + 0 + 270} 0.5 = {Var} 0.5.
=  {540} 0.5 = 23.24
How do we interpret this Result for Risk?
Standard Deviation Interpretation
What are the units of Standard Deviation?
For our example where Return is being estimated in % terms, the units of
Standard Deviation will also be %.
It tells us that if we assume a Normal Probability Distribution and symmetric about expected rate of
return, then we conclude that 68.26% of the time, the Actual Return will lie within -1 Standard
Deviation and +1 Standard Deviation of the Expected (or Mean) Return.
Expected (or Mean) Return = 10%
+/- 1 Standard Deviation = 10% +/- 23.24% which means from (10% - 23.24%) to (10% + 23.24%) i.e.
from -13.24% to 33.24%.
There is a 68.26% chance that the Actual Return on our Stock Investment after 1 year will be
somewhere between -13.24% and 33.24%. It is important thing to remember that in normal distribution
the area under the curve from -1 standard deviation to +1 standard deviation is 68.28%. So, we can be
sure that two thirds of the time the actual value for the return will be in between -13.68% and +33.24 %.
-13.24% is not a good sign as it indicates that we are making loss but remember that required rate of
return is 10%.
Graphical Standard Deviation
Expected (or Mean)
Return = <r> = 10%
+/- 1 Std Dev covers
68.26% of the Area
Prob
under the Normal
abili
Curve always
ty
(p)
Return (r) %
-2
-1
+1
+2
-13.24%
+33.24%
Our Example
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Financial Management ­ MGT201
VU
In the figure the probability is written on y-axis and the rate of return is mentioned on the x-axis.
It shows that higher the standard deviation the higher the risk.
Now, lets take a look another example in which we raw comparing three different investments
which we want to compare in terms of risk and return.
Example:
Comparison of 3 Investments in terms of Risk & Return. Which is the best Investment?
Risk (Std Dev)
Expected Return
Stock A
23.24%
10%
T-Bill/Bond B
5%
10%
Project C
30%
30%
T-Bill is Least Risky (lowest Std Dev =5%) and Project C has Highest Return (=30%).
Given 2 Investments with Identical Expected Return, choose the Investment with the Lower
Risk (or Spread or Volatility or Standard Deviation)
Given 2 Investments with Identical Risk, choose the Investment with the Higher Expected Return
If you compare first two investments, both have the same rate of return but the T-bills have less
risk. Clearly, T-Bill B is a better investment than Stock A because their Returns are identical (10%) but
the T-Bill is less risky (10%) than the Stock (23.24%).
But, which is better? T-Bill B or Project C? T-Bill B is Less Risky but Project C promises Higher
Return.
Now, we conceptually visualize these two types of investment
Combined Risk & Return
Graphical Comparison of Investments
T-Bill B: Low
Risk & Low
Proba
Return
bility
(p)
Project C: High
Risk B
Risk & High Return
Risk C
Exp Return C
Exp Return B
Rate of Return (r) %
In the figure, we are showing both investments on the same graph. Left hand shows the
probability distribution for the T- bills and on the right hand side shows the broader and shorter
probability graph for project C. How to visualize which project have higher expected rate of return.
Project C is on right hand side and therefore it has higher return as to project B.The other thing is that
project B form a probability distribution which have a sharp hill or spread of the curve is much narrower
as to project C. The standard deviation for project B is much narrower then the standard deviation for
project C .In project B has less risk whereas Project C has a higher expected rate return. We have to
look at risk and return simultaneously to answer that which option is better. We can derive the answer
with the help of the coefficient of variation
Comparison of Different Investments
Coefficient of Variation:
Coefficient of Variation (Risk per unit Return)
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Financial Management ­ MGT201
VU
It is defined as the CV = Standard Deviation / Expected Return. Coefficient of Variation tells us
about the Risk per unit Return. The project which offers lowest per unit risk is the best investment. Now
we calculate the CV for both the projects.
Compare the CV's of the Projects:
CV T-bill = 5% / 10% = 0.5
CV Project C = 30% / 30% = 1.0
Choose the Project with the Lowest CV. Choose the T-Bill because it carries the lowest Risk per unit
Return
Risk Aversion Assumption
Most Investors are psychologically Risk Averse. If two investments offer the same Expected
Return, most Investors would choose the one with the lower Risk (or Standard Deviation or Spread
or Volatility). In other words, most Investors are not major gamblers. Note that gamblers would
choose Project C which appeals to investor greed by offering an upside return of 30%+10% = 40% !
Consequences on Share Price: The Higher the Risk of a Share, the Higher its Rate of Return and the
Lower its Market Price.
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