1. Investments and Portfolio Management
Week 3 1

2. Risk and Return Objectives :
Discuss and be able to calculate how investors measure risk and return on an investment
Discuss the factors contributing to the rate of return required by investors, including macro and microeconomic factors
Understand the expected rate of return on equity markets 2

3. What is an Investment ?
Bodie,Z., Kane,A. and Marcus, A (2009) Investments, 4th edition, McGraw-Hill
“An Investment is the current commitment of money or other resources in the expectation of reaping future benefits” 3

4. Advanced definition of a monetary Investment
A current commitment of money for a period of time in order to derive future payments that will compensate for:
the time the funds are committed
the expected rate of inflation
uncertainty of future flow of funds. 4

5. Required and expected rates of return
The required rate of return is the minimum rate of return an investor requires on an investment, including all risk premiums to compensate the investor for taking the investment risk.
Investors may expect to receive a rate of return different from the required rate of return, which is called expected rate of return. 5

6. Required and expected rates of return
If expected rate < required rate sell/don’t buy If expected rate > required rate Keep/buy 6

7. Risk free rates of return
The nominal risk free rate of return (Rf) is the rate of return on a security, whose return is known in advance. This means that the investor will receive a known amount of cash. E.g. a government bond may have an annual coupon of 1.5%. This would be the risk-free rate. 7

8. Return premiums
The nominal risk-free rate is used to determine the market premium return (or the premium on any asset).
Recall CAPM:
ke = Rf + B (Rm – Rf)
Note: CAPM is one method of calculating a required rate of return
Market premium 8

9. Real rates of return 9

10. Real rates of return (cont.)10

11. Holding Period Yield 11

12. Holding Period Yield (cont.)12

13. Annualised Holding Period Yield
To compare the HPY of investments held over different periods, the annualised HPY can be calculated.
HPYA=HPR1/n - 1 (n=number of years of the investment)
Example: A stock that was bought for $25 received $3 in dividends over a two year period, after which it was sold for $26. What is the HPR and the annualised HPY?
Answer:
HPR = ($3 + $26)/$25 = 1.16
HPYA = 1.161/2 – 1 = or 7.7%
Proof: $25 * * = $29 13

14. Historical Rates of Return
Computing Mean Historical Returns
Suppose you have a set of annual rates of return for an investment. How do you measure the mean annual return?
Arithmetic Mean Return (AM)
AM= ( HPY) / n
where  HPY=the sum of all the annual HPYs
Geometric Mean Return (GM)
GM= [ HPR] 1/n -1
where  HPR=the product of all the annual HPRs 14

15. AM & GM Example Calculate the AM and the GM for the investment.
Suppose you invested £100 three years ago and it is worth £ today. The information below shows the annual performance over that time.
Calculate the AM and the GM for the investment.
Year Beginning Ending HPR HPY
Value Value
 HPY = 0.15 15

16. AM & GM Example (cont) AM = 0.15/3 = 5%
GM=[(1.15) x (1.20) x (0.80)]1/3 – 1
=(1.104)1/3 -1 =
= 3.353% 16

17. Comparison of AM and GM
When rates of return are the same for all years, the AM and the GM will be equal.
When rates of return are not the same for all years, the AM will always be higher than the GM.
While the AM is best used as an “expected value” for an individual year, the GM is the best measure of an asset’s long-term performance. 17

18. Expected Rates of Return using probability
Risk refers to the uncertainty of the future outcomes of an investment
There are many possible returns/outcomes from an investment due to the uncertainty
Probability is the likelihood of an outcome
The sum of the probabilities of all the possible outcomes is equal to 1.0. 18

19. Expected Rates of Return19

20. Expected Rates of Return - Example
Assume a purchase price of £100
Economic Forecast
Probability
Year end market price £
Cash dividend £
HPR
HPY
Boom
0.3
129.50
4.50
Current growth
0.5
110.00
4.00
Recession
0.2
80.50
3.50 20

21. Expected Rates of Return - Example
Assume a purchase price of £100
Economic Forecast
Probability
Year end market price £
Cash dividend £
HPR
HPY
Boom
0.3
129.50
4.50
( )/ = 1.34
0.34
Current growth
0.5
110.00
4.00
( )/ = 1.14
0.14
Recession
0.2
80.50
3.50
( )/ = 0.84
-0.16
Using HPR
E(Ri) = (0.3*1.34)+(0.5*1.14)+(0.2*0.84) = 1.14
Using HPY
E(Ri) = (0.3*0.34)+(0.5*0.14)+(0.2*-0.16) = 0.14 = 14% (HPR - 1) 21

22. Risk of Expected Return
Variance (σ2) å = - n i R E P
turn
Expected
Possible x
obability 1 2 )] ( [ ) Re
(Pr
The variance and standard deviation measure the dispersion of possible rates of return around the expected rate of return.
The larger the variance, the greater the dispersion of expected returns meaning greater uncertainty and, therefore, the greater the risk associated with the investment.
Note: If calculating mean and standard deviation for actual returns, replace ‘p’ with ‘1/n’ in the formulae 22

23. Risk of Expected Return
Standard Deviation (σ)
It is the square root of the variance
measures the total risk å = - n i R E P 1 2 )] ( [ s
Coefficient of Variation (CV)
It measures the risk per unit of expected return
relative measure of risk between investments with different expected rates of return. ) ( R E
Return of
Rate
Expected
Deviation
Standard CV s = 23

24. Example – Variance and Standard Deviation
E(Ri)= 0.14 24

25. Example – Variance and Standard Deviation25

26. Example – Variance and Standard Deviation26

27. Example – Coefficient of variation) ( R E
Return of
Rate
Expected
Deviation
Standard CV s =
Investment A
Investment B
Expected Return
0.14
0.11
Standard Deviation
0.173
0.152 CV 27

28. Example – Coefficient of variation) ( R E
Return of
Rate
Expected
Deviation
Standard CV s =
Investment A
Investment B
Expected Return
0.14
0.11
Standard Deviation
0.173
0.152 CV
0.173/0.14 = 1.236
0.152/0.11 = 1.382
Used by analysts to compare alternative investments with widely different rates of return and standard deviations of returns. 28

29. Risk Aversion
The assumption that most investors will choose the least risky alternative, all else being equal and that they will not accept additional risk unless they are compensated in the form of higher return Risk considers the likelihood of deviations from expected return 29

30. Elements of Fundamental Risk In Investing
Business risk
Uncertainty of income flows caused by the nature of a firm’s business
Sales volatility and operating leverage determine the level of business risk.
Financial risk
Uncertainty caused by the use of debt financing.
Borrowing requires fixed payments which must be paid ahead of payments to stockholders.
The use of debt increases uncertainty of stockholder income and causes an increase in the stock’s risk premium.
Liquidity Risk
Uncertainty is introduced by the secondary market for an investment.
How long will it take to convert an investment into cash?
How certain is the price that will be received? 30

31. Elements of Fundamental Risk In Investing
Exchange Rate Risk
Uncertainty of return is introduced by acquiring securities denominated in a currency different from that of the investor.
Changes in exchange rates affect the investors return when converting an investment back into the “home” currency.
Country Risk
Political risk is the uncertainty of returns caused by the possibility of a major change in the political or economic environment in a country.
Individuals who invest in countries that have unstable political-economic systems must include a country risk-premium when determining their required rate of return 31

32. Fundamental Risk versus Systematic Risk
Fundamental risk comprises business risk, financial risk, liquidity risk, exchange rate risk, and country risk
Systematic risk refers to the portion of an individual asset’s total variance attributable to the variability of a market benchmark, usually something we call the Market Portfolio. 32

33. Relationship Between Risk and Return
Movement along the Security Market Line (SML)
When the risk of an investment changes due to a change in one of its risk sources, the expected return will also change, moving along the SML.
Required
Return
SML
Movements along the curve Rf
that reflect changes in the
risk of the asset
Risk
Beta 33

34. Summary
Investments are a current commitment of money for a period of time in order to derive future payments that will compensate for time, inflation and uncertainty.
Historical rates of return can be measured on return which have been achieved in the past, or expected rates can be calculated based on probabilities of outcomes.
Variances and standard deviation can be used to determine the risk.

35. Reading Other relevant reading could include:
The slides for this week’s lecture have been based on:
Reilly, F. K. and Brown, K. C. (2012) Analysis of Investments and Management of Portfolios, 10th edition, Cengage Learning – Chapter 1
Stafford Johnson, R. (2014), Equity Markets and Portfolio Analysis, John Wiley & Sons – Chapters 3 & 6
Other relevant reading could include:
Bodie, Z., Kane, A. And Marcus, A. J. (2011) Investments and Portfolio Management, Global edition, McGraw-Hill Irwin – Chapter 5
Levy, H. And Post, T. (2005) Investments, FT Prentice Hall 35

36. Useful Bloomberg Functions
TRA <GO> analyses the historical total return for a selected equity
Control area
Strategy table
Price chart
Return chart 36

37. Useful Bloomberg Functions
SECF <GO> security finder – search for the ticker of the selected equity asset COMP <GO> shows cumulative HPR for a selected asset and allows its comparison against other assets or indices HRH <GO> shows distribution for a selected asset and displays mean and standard deviation (sigma) returns over a given time period 37