Global Equity Markets

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

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.

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.

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

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) =

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?

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) = 0.0910 = 9.10%

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)

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 0.10 - 0.063 = 0.037 (0.037)2 = 0.001369 3 111 (111 – 110) /110 = 0.01 0.01 - 0.063 = -0.053 (-0.053)2 = 0.002809 4 120 (120 – 111) /111 = 0.08 0.08 - 0.063 = 0.017 (0.017)2 = 0.000289 Mean (0.10 + 0.01+ 0.08) /3 = 0.063 (0.001369 + 0.002809 +0.000289)/3 = 0.001489

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

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

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)

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

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).

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

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!

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

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.

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

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

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 !!!!

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

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

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

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

ANY QUESTIONS?