Topic 2 – Risk and Return
2.1 The Components Of return
i. Yield – The periodic cash flows (or income) on the investment either interest or dividends. The issuer makes the payments in cash to the holder of the asset.
ii. Capital gain (loss) – The appreciation or depreciation in the price of the asset . i.e. the change in price on a security over some period of time.
Total Return = yield + capital gain. – A security’s total return consists of the sum of two components, yield and price change (capital gain). The price change can be negative. The yield cannot be negative.
Example:-
A bond purchased at par and held to maturity provides a stream of income in the form of interest payments. A bond purchased for RM 800 and held to maturity provides both a yield (income and a price change).
The purchase of a non-dividend paying stock that is sold months later produces either a capital gain or capital loss.
2.2 Realised Return and Expected Return
The measurement of actual (historical) returns is necessary for investors to assess how well they have done or how well investment managers have done on their behalf.
1. Realised Return – Actual return on an investment for some previous period of time. Return that was or could have been earned.
Example:-
A deposit of RM 100 in a bank of 1st January 2001 at a stated annual interest 6% was worth RM 106.00 one year later. The realized return for the year is 6.00/100.00 = 6%
2. Expected Return – The estimated return from an asset that investors anticipate (expect) they will earn over some future period. It is subject to uncertainty and may or may not occur. Investors should be willing to purchase a particular asset if the expected return is adequate.
3. Total return – Percentage measure relating all cash flows on a security for a given time period to its purchase price. Total return = (cash payments received + price changes over the period)/(price at which the asset is purchased).
TR = [CFt + (Pe – Pb)]/ Pb = (CFt + PC ) / Pb
Where
CFt = cash flows during the measurement period t
Pe = price at the end of period t or sale price.
Pb = purchase price of the asset or price at the beginning of the period.
PC = Change in price during the period or Pe – Pb.
Total return concept is valuable as a measure of return because it is all inclusive, measuring the total return per dollar of original investment. It facilitates the comparison of asset returns over a specified period.
4. Relative Return or Holding period Return (HPR) – The total return for an investment for a given time period stated on the basis of 1.0. The return relative will always greater than zero i.e. eliminating negative numbers.
Return relative = (CFt + Pe) / Pb or Total return + 1.
Calculate the total return and return relative for the following examples.
Example 1
Assume the purchase of a 10% coupon Treasury Bond at a price of RM 960, held one year and sold for RM 1020.
TR = [100 + (1020 – 960)] / 960 = (100 + 60 ) / 960
= 0.1667 @ 16.67 %
RR = (100 + 1020) / 960 = 1.1667
Example 2
1000 shares of ABC Bhd are purchased at RM 30 per share and sold one year later at RM 26 per share. A dividend of RM 2 per share is paid.
TR = [2 + (26 – 30)] / 30 = (2 +(-4) / 30
= -0.0667 @ -6.67%
RR = (2 + 26 ) / 30 = 0.9333
Example 3
Assume the purchase of warrants of ABC Bhd at RM 3 each, a holding period of six months and the sale at RM 3.75 each.
TR = [0 + (3.75 – 3.00)] / 3.00 = 0.75 / 3.00
= 0.25 @ 25%
RR = 3.75 / 3.00 = 1.25
TR = RR – 1 or Holding Period Yield (HPY)
Annual HPR = HPR 1/n
where n = number of years the investment is held.
Example 4
You bought Malayan banking Bhd shares at RM 20.00 per share in year 1 and received A dividend of 15 sen. You than sold the shares in year 2 at RM 25.00 per share.
HPR = (0.15 + 25.00) / 20.00 = 1.2575
HPY = HPR – 1
= 1.2575 – 1 = 0.2575 @ 25.75%
Example 5
An investor purchased Malaysia Airline System Bhd shares at RM 6.00 in year 1 and sold them at RM 10.00 in year 2. assuming that he received a dividend of 7 sen in year 1 and 8 sen in year 2. What is the annual HPR.
HPR = [(Dividend of year 1 + year 2 ) + (share price in year 2)] / cost of investment
= [(0.07 + 0.08) + 10] / 6
= 1.69
Annual HPR = (1.69) 1/n
= (1.69) ½
= 1.3
Annual HPY = 1.3 – 1 = 0.3
= 30 %
5. Arithmetic Mean – As the simple average of all HPYs.
Arithmetic mean = (sum of annual holding period yields ) / (no. of years during
which the investment was held).
= ∑ HPY / n
6. Geometric Mean – It measures the ‘true’ average rate of return over multiple periods. It indicates the compound annual rate of return based on the ending value of the investment versus its beginning value. It is defined as the nth root of the product resulting from multiplying a series of returns together.
Geometric Mean = [(1 + r1) (1 + r2) …(1 + rn)] 1/n – 1 @
Geometric Mean = [ (1 + HPY 1)(1 + HPY2) … (1 + HPY n)] 1/n – 1
= [(HPR 1)(HPR2) …..(HPRn)] 1/n – 1
HPR = Holding period return
n = number of years
* The arithmetic mean return is a good indication of the expected rate of return for an investment during an individual year.
The Geometric Mean return is generally considered to be a superior measure of long-term mean rate of return.
Investors are usually concerned with the long-term performance of their investments.
Example 6
Consider an investment in Berjaya Group Bhd with the following data :
year Beginning Value
RM Ending value
RM HPR HPY = (HPR -1)
1 1.00 1.50 1.50 0.50
2 1.50 2.00 1.33 0.33
3 2.00 1.60 0.8 -0.20
Assuming no dividend income during the holding period.
HPR 1 = 1.50/ 1.00 = 1.50
HPR 2 = 2.00 / 1.50 = 1.33
HPR 3 = 1.60 / 2.00 = 0.80
Arithmetic mean = ∑ HPY / n
= (0.5 + 0.33 – 0.2 ) / 3
= 21 %
Geometric Mean = [(HPR 1)(HPR 2) (HPR 3)] 1/n – 1
= [(1.50) (1.33) (0.8)] 1/3 – 1
= [1.6] 1/3 – 1
= 1.17 -1
= 17%
Example 7
Use the above example with the following data.
Year Beginning Value
RM Ending Value
RM HPR HPY = ( HPR -1)
1 1.00 2.00 2.00 1.00
2 2.00 1.00 0.50 (0.50)
Assuming no dividend income is paid during the holding period of the investment.
HPR 1 = 2.00/1.00 = 2.00 HPY 1 = 2 -1 = 1
HPR 2 = 1.00 / 2.00 = 0.5 HPY 2 = 0.50 – 1 = (0.50)
Arithmetic mean = [ 1.00 + (0.50)] / 2
= 0.25
= 25%
Geometric mean = [(2.00) (0.50)] ½ - 1
= [1.00] ½ - 1
= 1.00 – 1
= 0%
• The arithmetic mean rate of return gives 25% return when there is actually no increase in the value of share price.
• Geometric mean has accurately indicated that there is no change in the investment value.
HOLDING PERIOD RETURN
Investors tend to hold their investment in assets for a period of time. Some may hold the
investments for a shorter period like three months or six months, while others may hold them
for a longer period like two years or five years. The total return of their investment for holding
them for a certain time period is called the holding period return. This holding period return
can be computed as follows:
HPR = Ct +(Ending price –Purchase price )
Purchase price
Example 1
You purchased 500 shares of Sime Darby Bhd. at RM5.80 per share and held the shares for
two years. During this period, you received dividends of RM0.15 per share and then sold the
shares for RM6.20 per share. The holding period is two years and the holding period return
can be computed as follows:
Therefore: HPR = Income + Price Difference
Purchase price
Example 2
You purchased 1,000 shares of IGB Bhd. at RM1.50 per share and held the shares for one
month. During this period, you did not receive any dividends but the price has now gone up
to RM1.60 per share. If you sell the shares, your holding period return would be:
From Example 1 and Example 2, it can be seen that the holding period can differ two years in
Example 1 and one month in Example 2 depending on the investor’s decision as to when to
sell off their shares. Since the holding period may differ, it is difficult to make comparisons on
the performance of investments with different holding periods. Thus to compare the performance of investments with different holding periods, one has to convert all investment returns on the standard scale, that is on the annual holding period basis. This is called
annualising a holding period return and can be done as follows:
Annualised HPR = ( 1 + HPR ) 1/ n _ 1
Where n is the number of years in the holding period.
Referring to Example 1, the annualised HPR for Sime Darby Bhd. shares is as follows:
Annualised HPR = (1 + 0.0948) ½ _ 1
= (1.0948) ½ _ 1
= 0.0463
= 4.63%
HPR = RM0.15 + (RM6.20 _ RM5.80) x 100
RM5.80
= 9.48%
HPR = (RM1.60 _ RM1.50) x 100
RM1.50
= 6.67%
2.3 Risk
Risk and return go together in investments and finance. Investment decisions involve a tradeoff between the two.
Definition – The chance that actual outcome from an investment will differ from the expected outcome. The more variable the possible outcomes that can occur the greater the risk.
2.4 Sources Of Risk
1. Interest rate risk
The variability in a security’s return resulting from changes in the level of interest rates. The changes affect all securities inversely. i.e. other things being equal, security prices move inversely to interest rates. It affects bonds more directly than common stocks and is a major risk faced by all bondholders.
2. Market risk
The variability in returns resulting from fluctuations in the overall market i.e the aggregate stock market. All securities are exposed to market risk.It includes a wide range of factors exogenous to securities including recession, wars, structure change in the economy and changes in consumer preferences.
3. Inflation risk
It is about purchasing power risk or the chance that the purchasing power of invested dollars will decline with uncertain inflation , the real return involves risk even if the nominal return is safe. It is related to interest rate risk, since interest rates generally rise as inflation increases because lenders demand additional inflation premiums to compensate for the loss of purchasing power.
4. Business risk
The risk of doing business in particular industry or environment.
5. Financial risk
It is associated with the use of debt financing by companies. The larger the proportion of assets financed by debt, the larger the variability in the returns, other things being equal. It involves financial leverage.
6. Liquidity risk
It is the risk associated with the particular secondary market in which a security trades. An investment that can be sold quickly and without significant price concession is considered liquid. The more uncertainty about price concession, the greater the liquidity risk.
7. Exchange rate risk
All investors who must internationally face the prospect of uncertainty in the returns after they convert the foreign gains back to their own currency. It can be defined as the variability in returns on securities caused by currency fluctuations . Sometime called as currency risk.
8. Country risk
Referred as political risk . Investors who are investing internationally direct or indirectly must consider the political, economic and stability and variability of a country’s economy.
2.5 Types of risk or The Components of risk
1. Unsystematic risk (nonmarket risk)
It is not related to overall market variability. This is the risk that is unique to a particular security and is related to factors such as business and financial risks Risk attributable to factors unique to a security.
2. Systematic risk (market risk)
Risk attributable to broad macro factors affecting all securities. It encompasses risks like interest rate risk, market risk, inflation risk etc. It is unavoidable and cannot be diversified. If the market rises strongly (a bull market) , most of the stocks will appreciate in value and when the stock market declines sharply (a bear market0, most of the stocks will depreciate in value. All securities have some systematic risk.
Total risk = systematic risk = unsystematic risk.
2.6 Diversification of risk
An investor can construct a diversified portfolio and eliminate part of the total risk i.e the diversifiable or nonmarket part (unsystematic risk). After the unsystematic risk is eliminated what is left is the non diversifiable portion or market risk (systematic risk). Market risk is inescapable. It is the risk of the overall market cannot be avoided.
2.7 Expected Risk and Return
Expected Return
Definition – It is the average of all possible return outcomes, where each outcome is weighted by its respective probability of occurrence.
n
ERi = ∑ Xi P(Xi)
i=1
Where
ERi = the expected return for security i.
Xi = the value of the it possible outcome.
P(Xi) = the probability of the it possible outcome
n = the number of possible outcome.
Estimating Risk
Standard deviation is being used in estimating total risk associated with the expected return.
n
S = √ ∑ [(Xi – ERi) 2 . P(Xi)]
i=1
where
S = standard deviation
Example 1
Calculate the expected return and total risk from the following data.
Possible return (Xi) Probabality P(Xi)
1% 20%
7% 20%
8% 30%
10% 10%
15% 20%
i. ERi = (0.01 x 0.2) + (0.07 x 0.2) + (0.08 x 0.3) + (0.1 x 0.1) + (0.15 x 0.2)
= 0.08
ii. Calculation of standard deviation
2.8 Capital Asset Pricing Model (CAPM)
• CAPM relates the required rate of return for any security with the risk for that security as measured by beta.
• Beta is the relevant measure of risk that cannot be diversified away in a portfolio.
• Beta is the measure that investors should consider in their portfolio management decision process.
Ki = RF + ßi [E(Rm) – RF]
Where
Ki = the required rate of return on asset i.
E(Rm) = the expected rate of return on the market portfolio.
ßi = the beta coefficient for asset i.
RF = risk-free rate
Market risk premium = E(Rm) – RF
Risk premium is the difference between the expected return for the market and the risk-free rate of return.
Assumptions:-
1. All investors have identical probability distributions for future rates of
return.
2. all investors have the same on-period time horizon.
3. All investors can borrow or lend money at the risk-free rate of return.
4. There are no transaction costs.
5. There are no personal income taxes.
6. There is no inflation.
7. No single investor can affect the price of a stock through his or her buying
and selling decisions.
8. Capital markets are in equilibrium.
Therefore risk premium for security i = ßi (market risk premium)
= ßi [E(Rm) – RF]
Examples;
If Rm = 15%; RF = 5%. The beta values for each security are as below.
ßA = 1.5 ; ßB = 1 ßC = 0.5 ßD = 0
Calculate the required rate of returns for each security.
Example :
TEN Bhd. has a beta coefficient of 0.5. If the market risk premium is 11%, determine the expected return for TEN Bhd.
E (rTEN) = rRF + β
i (E (rm) – rRF)
Given market risk premium = (E (rm) – rRF) = 11%
Therefore, E (rTEN) = 4% + 0.5 (11)% = 9.5%
2.9 Security Market Line (SML)
SML shows the trade-off between risk and expected return for all assets.
SML is the graphic representation of CAPM.
(a) In equilibrium where supply and demand are equal, all the returns of the securities will lie
on the SML.
(b) If the market is not in equilibrium, the estimated return of security will either lie below or
above the SML.
• In equilibrium each security should lie on the SML.
• If a security does not lie on the SML, what happens in the market.
• An investor might use other methods to determine the expected returns
for securities.
• The investor can assess a security in relation to the SML and determine
whether it is under or over valued.
• From the figure, security X has a high expected return derived from
fundamental analysis and plots above the SML. Security Y has a low
expected return and plots below the SML.
• Security X is undervalued because it offers more expected return than
investors require.
• Investors will do :-
Purchase security X. This demand will drive up the price of X. The return will be driven down until it is at the level indicated by the SML.
• Security Y is overvalued. It does not offer enough expected return as
required by investors.
• Investors will do :-
Sell security Y. This increase in the supply of Y will drive down its price. The return will be driven up because any dividends paid are now relative to a lower price. The price will fall until the expected return rises enough to reach the SML.
2.10 Risk- Return Relationship
• The risk-return tradeoff is the foundation of investment decisions.
• The tradeoff depicts a positive linear relationship between expected return
and risk.
• Risk-averse investor will not willingly assume more risk unless they expect to receive additional return.
The relationship between return and risk expected as below:-
1. The expected return should be positively related to the risk.
2. Over long period of time , the historical relation between return and risk should be positive.
3. Over relatively short periods; the tradeoff between return and risk is always expected to be positive but it may turn out to b
