1. Global Equity Markets

2. WEEK 4
Arnold (2013). Corporate Financial Management. Pearson. (Chapter 7)
Return and Risk
Portfolio Diversification
Portfolio Extensions to Many Assets
Efficient Portfolios

3. SOURCES OF RISK
There are two broad sources of risk – Economic or Financial. Economic risks relate to macroeconomic conditions.
Political Risk and Regulatory Risk
Exchange Rate/Currency Risk
Labour Risk
Liquidity Risk and Insolvency Risk
Overall, risk can be defined as the probability distribution of a series of possible economic outcomes.

4. RISK AND UNCERTAINTY
With both uncertainty and risk we are considering situations where there are more possible outcomes than will actually occur.
A range of possible outcomes may occur; but, after undertaking the project, only one outcome will occur.
 Risk: refers to a state where the decision maker has sufficient information to determine the probability of each possible outcome occurring.
Uncertainty: the decision maker can identify each possible outcome, but does not have the information necessary to determine the probabilities of each outcome.

5. RISK ATTITUDES Depending upon their nature, investors could be:
Risk Averse
Risk Neutral
Risk Lover
Attitude can be determined via an actuarially fair gamble.
Risk attitudes affect an investors decision to diversify investment in order to hedge against:
Systematic Risk – non-diversifiable risk
Unsystematic Risk – diversifiable or firm-specific risk

6. EXPECTED RETURNS
Expected returns are the anticipated probability of a return on an investment.
The return on investment in stocks (shares) comes in two forms:
Dividends
Capital Gain (or Loss)
It is calculated as follows:
E(R) =

7. What is the expected return of this investment?
Scenario
PRs
Holding Period
Boom
0.10
£0.31
Good
0.25
£0.14
Poor
0.40
-£0.07
Crash
-£0.52
What is the expected return of this investment?

8. EXPECTED RETURN The expected return is calculated as:
So, the expected return of this investment is:
E(R) = (0.10 x £0.31) + (0.25 x £0.14) + (0.40 x [-£0.07]) +
(0.25 x [-£0.52])
E(R) = = 9.10%

9. RISK AND RETURN
Under normal market conditions, the mean and variance provide good measures of the return and risk associated with any investment
The mean (or expected value)
The variance (2)

10. Calculate the mean & variance of returns
Period
Share Price
Return
Deviation
Variance 1
100
Return - Mean
(Deviation) 2 2
110
(110 – 100) /100 = 0.10
= 0.037
(0.037)2 = 3
111
(111 – 110) /110 = 0.01 =
(-0.053)2 = 4
120
(120 – 111) /111 = 0.08
= 0.017
(0.017)2 =
Mean
( ) /3 = 0.063
( )/3 =

11. Choosing between risky assets
A crucial question is:
how do investors choose between different investments which offer different combinations of risk and return?
If two investments have same expected return and one has higher risk then investor will prefer the project with lower risk.
For same level of risk a project with higher expected rate of return will be preferred

12. Portfolio Diversification
We can use the probability theory to determine the mean (expected return) and variance (risk) of the JOINT distribution of several stocks (portfolio)
Need to specify (i) mean, (ii) variance and…(iii) covariance of the individual stocks
Result:
It can be shown that risk, as measured by variance, is reduced by holding a diversified portfolio

13. Two asset portfolios Portfolio risk and return
Consider a portfolio consisting of two assets 1 and 2. The individual invests proportion x1 in company 1 and x2 in company 2
Expected return on portfolio:
Variance of portfolio:
Proportion of investment in each asset, 1 and 2
Variance of each asset, 12 22
Covariance between them, cov(R1 R2)
(1)
(2)

14. THE CORRELATION COEFFICIENT
Thus, equation (2) can be rewritten as:
(3)

15. PORTFOLIO CORRELATION
If the correlation between two securities is -1, then the stocks are said to be perfectly negatively correlated (i.e. they move in opposite directions perfectly).
If it is +1, then they are perfectly positively correlated (i.e. they move in perfect harmony).
If it is 0, then they are uncorrelated (i.e. they do not move together).

16. Implications of Diversification
Expression (3) consists of,
The proportion of wealth invested in each asset
The standard deviation (risk) of each asset
ρ12, the correlation coefficient between the two assets
Correlation, ρ12, can be +ve or –ve ; and -1  ρ12  1
Thus
If ρ12= 0 the portfolio risk is given by the sum of the asset variances only

17. Implications of Diversification
If ρ12= 1 there is no risk reduction effect from holding both assets
If ρ12= -1 maximum risk reduction effect
What is true for a two-assets portfolio is also true to a multiple asset portfolios:
by investing in assets which have a correlation coefficient less than 1 the overall risk can be reduced
As ρ12 moves further away from +1 the risk reduction effect becomes greater!

18. Diversifiable and non-diversifiable risk
Portfolio risk (p)
Diversifiable (non-systematic) (firm-specific) risk
Non-diversifiable (systematic) (market) risk
No. of assets in portfolio

19. The Effects of Diversification
Firm-specific risk can be reduced, if not eliminated, by increasing the number of investments in your portfolio (i.e., by being diversified). Market risk cannot!
This can be justified on either economic or statistical grounds.
On economic grounds, diversifying and holding a larger portfolio eliminates firm-specific risk.

20. Multiple asset portfolios
The analysis can be extended to portfolios of many assets, but the calculations become complicated especially in relation to portfolio risk
The full set of variances and covariances have to be taken into consideration
Thus for a three asset portfolio we have nine elements in the calculation of risk
However, a graphical approach can be adopted

21. A three asset portfolio risk-return trade-off
Expected Return E(Rp)
E(R2) W
efficient frontier A
E(R1) Y Z
minimum variance portfolio
DZWA represents the “efficient frontier / boundary:
 The set of portfolios with the highest return for a given level of risk B D C σ1 σ2
Risk σp

22. Portfolio with a risk-free asset
Consider the introduction of a risk-free asset
e.g. Proxies: Treasury bills, Government Bond, etc.
“Safety Heaven” securities
Characteristics:
Guaranteed return : E(rf) = rf , but tend to be quite modest
Standard deviation : σf = 0 !!!!

23. Portfolio of a Risky Asset A and Risk-Free Asset
Expected return:
Variance (risk):
Portfolio risk depends only on the standard deviation of (and the proportion invested in) the risky asset A

24. Efficient frontier with one risky asset and a risk–free asset
E(Rp) A
E(rA)
Slope of the line is
The incremental expected return for an additional unit of risk rf σA σp

25. The market price of risk
The equation for the CML gives the expected return from an efficient portfolio and is written,
Where λ = market price of risk

26. THE ASSUMPTIONS The assumptions upon which the analysis is based
Maximisation of utility from wealth
Choices are based on expected return and risk
Unlimited borrowing and lending at rf
Perfect markets, no taxes or transactions costs
Perfect information available to all investors
Decision-making time horizon same for all investors

27. ANY QUESTIONS?