CHAPTER 3
RISK AND
RETURN
Return in Investment
Components of
Investment Return
Return and Risk
Calculation
Historical Rate of
Return
- Holding Period Return
- Holding Period Yield
- Mean Historical Return
Expected Rate of
Return
Risk Calculation for
Single Asset
Risk &
Return for Portfolio
Asset
Correlation
Diversification
Concept
Capital Asset Pricing
Model (CAPM)
Required Rate of
Return, Risk Free Rate & Beta
Market Premium
3.0 INTRODUCTION
The decision making process in investment
strongly depends on the risk and return offered by instruments.
The exposure of risk also differ based on the financial market
itself. For example, normally capital
market instruments are riskier as compared to money market instruments. Therefore, to compensate the risk, capital
market will offer higher return relatively to money market.
3.1 RETURN IN INVESTMENT
In investment, return refers to income or money
that a person or company earns as a percentage of total value that has invested
for a particular period of time. In a
simple words, return means how much investors earn or profit they make
from their initial investment in any investment.Besides, Risk is often understood as the
possibility of loss. In financial terms, risk also refers to a range of
possibilities and the variability of returns and degrees of uncertainty.
For example, Nur Aini has invested RM 1000.00 in unit
trust early 2011 and the value increased to RM 1200.00 in January 2012. The return of the investment should be
RM200.00 (RM1200-1000); or; the
Holding Period Return (HPR) will be;
Return on investment for HPR =
3.2 COMPONENTS OF
INVESTMENT RETURN
There are two types
of return in investment:-
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i.
Dividend Income /Yield/
Coupon Rate / Interest – Periodical income
over investment period.
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ii.
Capital Incomewhich is refers to
the differnces between purchasing and selling price of intruments.
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For example; Assume that Mr.Ali has bought 50 lot
of Zero to Hero Corporation stock in early 2007 at RM2.00 per share. He intended to sell those stocks at the end
of year 2011(right after the dividend declaration). Based on the information
given, compute the total income of Mr. Ali’s investment.
The dividend declared are as follows:-
|
End of Year
|
%Dividend (Yield)
|
Share Price
|
|
2007
|
10%
|
2.00
|
|
2008
|
12%
|
2.50
|
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2009
|
5%
|
1.50
|
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2010
2011
|
10%
15%
|
1.80
2.30
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* 1 Lot = 100 shares
Therefore, the total
income of investment in Zero to Hero Corporation would be:-
|
End of Year
|
Dividend (%)
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No. Of Shares
|
Dividend earnings
|
Buying Price
|
Selling Price
|
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2007
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10%
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5000
|
500
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2.00
|
|
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2008
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12%
|
5000
|
600
|
|
|
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2009
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5%
|
5000
|
250
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|
|
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2010
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10%
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5000
|
500
|
|
|
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2011
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15%
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5000
|
750
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2.30
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|
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Dividend Income
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RM2600
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|
|
|
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Capital Income:
[(2.30 -2.00)*5000]
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RM1500
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|||
Total Income = Dividend Income + Capital Income
(RM2600+RM1500) =RM4100
3.3 RETURN CALCULATIONS
The return on investment can be measuredin two
different method using historical and
expected data to derive Historical
Rates of Return and Expected Rates of Return.
3.3.1 Historical Rates of Return
Investors use this method to compute their rates
of return for the investment that they have made in previous year/s to calculate
their Holding Period Return (HPR) and Holding Period Yield (HPY).
i.
Holding Period Return
(HPR)
Holding period return is a very basic calculation to measure
how much return investors have gained on a particular investment. HPR is the total
return from an investment, including all sources of income for a given period
of time.
Example1: Assume
that you have invested RM350.00 at
begining of the year and at the end of the year, the value of investment
increased to RM400.00. in this example the HPR is 1.142, calculated
as follows:-
HPR = 400/350
HPR = 1.142
Example 2: Mr. Y has
invested RM250 in year 2009 and now the investment worth RM350 after being held
for two years, compute:-
a) the HPR = 350/250
=1.40
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n = numbers of years the investment is held.
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= HPR1/n
=1.401/2
= 1.1832
Note that HPR value will always be zero or
greater and cant never be a negative value.
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HPR
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Indicator
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HPR > 1
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Increase in asset
value
Increase in
investors wealth
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HPR< 1
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Decrease in asset
value
Decrease in investors
wealth
|
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HPR = 0
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Loss all the money
in investment
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HPR= 1
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The value of
investment did not change
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HPR is one of useful tool for investors to track
their investment performance from time
to time as well as to evaluate the value
of investment.
ii. Holding Period Yield (HPY)
HPY is a return of investment in percentage terms
on an annual basis. HPY is derived from
HPR minus 1.
(using the
same example 1, the HPY of your investment would be = 14.2%)
HPY =
HPR -1
= 1.142 -1
= 14.2%
For any investment which has longer period more
than one year, investor can use Annual HPY to compare their performace for any
particular year.
Annual HPY = Annual HPR - 1 ;
Where, Annual HPR= HPR1/n
Annual HPY = HPR1/n – 1
Refer to Example 2: Mr. Y has invested RM250 in
year 2009 and now the investment worth RM350 after being held for two years,
compute:-
Annual HPY = 350.00
½- 1
250.00
= 1.18 - 1
= 18%
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Tips 1
Assume the HPY of an investment is 15%, what is the HPR?
HPY
= HPR-1 ; HPR = HPY + 1
HPR = 0.18 + 1
HPR = 1.18
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iii. Mean Historical Return
Investor also can evaluate series of
past performance of a security or index
to predic future returns or to estimate how securities might react to
any particular situation in the future using both Arithmethic Mean (AM) and
Geometric Mean (GM).
a)
Arithmethic Mean (AM)
Also known as Arithmetic
Average Return. AM is a measure of
mean annual rates of return equal to the sum of annual holding period rate of
return devided by numbers of years.
where
= the sum
of annual HPY.
b)
Geometric Mean (GM)
Known as Geometric
Mean Return. GM is used to determine the performance results of an
investment or portfolio.
Where;
= the product of annual HPR as follows:
= (HPR1) x (HPR2)
x (HPR3) x.....x (HPRn)
Example: Table below shows the data of investment in Security A in year
1, 2 and 3:
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Year
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Beginning
|
Ending
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HPR
|
HPY
|
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1
|
200
|
250
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250/200 =1.25
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0.25
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2
|
250
|
230
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230/250 =0.92
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-0.08
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3
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230
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280
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280/230 =1.22
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0.22
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AM =
= [(HPY1) + (HPY2)
+ (HPY3)] / 3
= [(0.25) + (-0.08) + (0.22)] /
3
= 0.13 = 13%
GM =
1/n -1
= [(1.25) x (0.92) x (1.22)]1/3
- 1
= 1.4031/3 – 1
= 0.119 = 11.9%
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Tips 2
GM is considered as a superior measure of
the long-term mean rate of return because it indicate compounded annual
return based on the ending value of investment versus the begining or
initial investment.
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3.3.2 Calculating
Expected Rates of Return
In the situation which investors did not
have any historical data on the investment, they can use the expected rate of return
to decide whether to invest or not to invest in particular asset. The Expected Rates of Return (ERR) is a
projected percentage return on an investment, based on the weighted probability
of all possible future rates of return.
This rate will be the basis of investor’s expectation toward the
performance of an asset in the future.
ERR is
calculated by the following formula:
The following example
illustrates the principle that the formula expresses:
Example 1: Assume
the current price of ABM, Inc. stock is trading at RM10. The economic conditions
and returns are as follows:
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Economic Condition
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Probability
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Return
(%)
|
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Strong
|
0.25
|
30
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Weak
|
0.50
|
20
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Not Change
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0.20
|
30
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To
find the expected rate of return, simply multiply the percentages by their
respective probabilities and add the results:
Example 2: Table below
shows the investment return of 3 assets/markets based on different economic
situations, compute the ERR for each asset.
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State
of Economy
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Probability
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Return
|
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Money Market
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Derivatives market
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Government Bond
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Deep Recession
|
0.05
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6.0%
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-27.0%
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10.0%
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Mild Recession
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0.20
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3.0%
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-5.0%
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6.0%
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Typical Economy
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0.50
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2.0%
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9.0%
|
4.0%
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Mild Boom
|
0.20
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1.0%
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23.0%
|
2.0%
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Strong Boom
|
0.05
|
-2.0%
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45.0%
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-2.0%
|
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Therefor; ERR =
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Expected Rate of Return =
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2.0%
|
9.0%
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4.0%
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Calculations:
- FURTHER READING: Refer to-------
