Risk and Return

LECTURE 2

Risk and Return
Twin axioms of modern financial theory
Fear
• Risk averse • Degree of risk aversion

Greed
• Non-satiable appetite for wealth • Utility

Risk Aversion
• Behaviour when exposed to uncertainty • Risk attitudes:
– Risk averse (or risk avoiding) – Risk neutral – Risk loving (or risk seeking)

• Measurements: additional marginal reward an investor requires to accept additional risk
– Absolute risk aversion – Relative risk aversion

Utility
• Satisfaction experienced when consuming a good • Expected utility theory deals with choices of risky projects with multiple outcomes

Risk
• Typically, investment returns are not known with certainty • Investment risk refers to the probability of earning a return less than that expected • The greater the chance of a return far below the expected return, the greater the risk

Return
• Investment returns measure the financial results of an investment • Returns may be historical or prospective (anticipated/expected) • Can be expressed in units of currency (dollars or RM) or percentage terms

Risk, Return and Financial Markets
• We can examine returns in the financial markets to help us determine the appropriate returns on non-financial assets • Lessons from capital market history
– There is a reward for bearing risk – The greater the potential reward, the greater the risk – This is called the risk-return trade-off

The Importance of Financial Markets
• Financial markets allow companies, governments and individuals to increase their utility
– Savers have the ability to invest in financial assets so that they can defer consumption and earn a return to compensate them for doing so – Borrowers have better access to the capital that is available so that they can invest in productive assets

• Financial markets also provide us with information about the returns that are required for various levels of risk

Dollar Returns
• Total dollar return = income from investment + capital gain (loss) due to change in price • Example:
– You bought a bond for RM950 one year ago. You have received two coupons of RM30 each. You can sell the bond for RM975 today. What is your total dollar return?
• Income = 30 + 30 = 60 • Capital gain = 975 – 950 = 25 • Total dollar return = 60 + 25 = RM85

Percentage Returns
• It is generally more intuitive to think in terms of percentages than in dollar returns • Dividend yield = income / beginning price • Capital gains yield = (ending price – beginning price) / beginning price • Total percentage return = dividend yield + capital gains yield

Calculating Returns
• You bought a share for RM35 and you received dividends of RM1.25. The share is now selling for RM40.
– What is your dollar return?
• Dollar return = 1.25 + (40 – 35) = RM6.25

– What is your percentage return?
• Dividend yield = 1.25 / 35 = 3.57% • Capital gains yield = (40 – 35) / 35 = 14.29% • Total percentage return = 3.57 + 14.29 = 17.86%

Holding Period Return
• The holding period return is the return that an investor would get when holding an investment over T periods, when the return during each period i is given as Ri:
HPR (1 R1 ) (1 R2 )  (1 RT ) 1

Holding Period Return
• Suppose your investment provides the following returns over four quarters:
Q 1 2 3 4 Return 10% -5% 20% 15%

Your holding period return (1 R1 ) (1 R2 ) (1 R3 ) (1 R4 ) 1 (1.10) (.95) (1.20) (1.15) 1 .4421 44.21%

Return Statistics
• The history of capital market returns can be summarized by describing the: – average return ( R1  RT ) R T – the standard deviation of those returns
R) 2  ( RT SD VAR T 1 – the frequency distribution of the returns ( R1 R) 2 ( R2 R) 2

Value of $100 Invested from 1925

Source: Chicago Center for Research in Security Prices, Standard and Poor’s, MSCI, and Global Financial Data.

Empirical Distribution of Annual Returns 1926–2011

Average Annual Returns 1926–2011

Value of $100 Invested for Alternative Investment Horizons

Source: Chicago Center for Research in Security Prices, Standard and Poor’s, MSCI, and Global Financial Data.

Risk Statistics
• There is no universally agreed-upon definition of risk. • The measures of risk that we discuss are variance and standard deviation. – The standard deviation is the standard statistical measure of the spread of a sample, and it will be the measure we use most of the time. – Its interpretation is facilitated by a discussion of the normal distribution.

Normal Distribution
• A large enough sample drawn from a normal distribution looks like a bell-shaped curve.
Probability

–3

–2

–1

0 μ 68.26% 95.44% 99.74%

+1

+2

+3

Return on large company stocks

Variance and Standard Deviation
• Variance and standard deviation measure the volatility of asset returns • The greater the volatility, the greater the uncertainty • Historical variance = sum of squared deviations from the mean / (number of observations – 1) • Standard deviation = square root of the variance

Variance and Standard Deviation
Year Actual Return Average Return Deviation from the Mean Squared Deviation

1
2

.15
.09

.105
.105

.045
-.015

.002025
.000225

3
4 Totals

.06
.12

.105
.105

-.045
.015 .00

.002025
.000225 .0045

Variance = .0045 / (4-1) = .0015

Standard Deviation = .03873

Volatility 1926–2011

Risk Premiums
• The “extra” return earned for taking on risk • Treasury bills are considered to be risk-free • The risk premium is the return over and above the risk-free rate resulting from bearing risk. • One of the most significant observations of stock market data is the long-run excess of stock return over the risk-free return.

Volatility vs. Excess Return 1926–2011

Arithmetic vs. Geometric Mean
• Arithmetic average – return earned in an average period over multiple periods • Geometric average – average compound return per period over multiple periods • The geometric average will be less than the arithmetic average unless all the returns are equal • Which is better?
– The arithmetic average is overly optimistic for long horizons – The geometric average is overly pessimistic for short horizons – So the answer depends on the planning period under consideration • 15 – 20 years or less: use arithmetic • 20 – 40 years or so: split the difference between them • 40 + years: use the geometric

Computing Averages
• Recall our earlier example:
Q 1 2 3 4 Return 10% -5% 20% 15%

Geometric average return (1 Rg ) 4 Rg
4

(1 R1 ) (1 R2 ) (1 R3 ) (1 R4 )

(1.10) (.95) (1.20) (1.15) 1

.095844 9.58%

So, our investor made an average of 9.58% per quarter, realizing a holding period return of 44.21% for that year. 1.4421 (1.095844) 4

Computing Averages
• Note that the geometric average is not the same as the arithmetic average:
Q 1 2 3 4 Return 10% -5% 20% 15%

Arithmetic average return

R1 R2 4

R3

R4

10% 5% 20% 15% 10% 4

Risk-Return Tradeoff Large Portfolios

Source: CRSP, Morgan Stanley Capital International

Risk-Return Tradeoff Individual Stocks

Unlike the case for large portfolios, there is no precise relationship between volatility and average return for individual stocks. Individual stocks have higher volatility and lower average returns than the relationship shown for large portfolios.

Types of Risk
• Idiosyncratic risk (Unique/Firmspecific/Unsystematic/Diversifiable)
risk that only affects individual firm Can be eliminated by diversification

• Systematic risk (Market/Non-diversifiable)
risk that affects the whole economy or market Cannot be eliminated by diversification