
Percentage return
 Percentage return: the sum of the cash received and the change in value of the asset, divided by the initial investment.
 Dividend + ending market value  beginning market value)/ beginning market value

Average return
 Average year return for stock.
 Sum of return for each period/ number of periods.
 Calc: type in each number followed by sigma, then press down shift 7

Holding period returns
 Total return on the investment
 HPR= (1 + return1) x (1+return2).... 1

What is risk?
 How certain you are that you will receive a particular return. Higher risk means you are less certain.
 Risk can be defined as the uncertainty of the future outcomes of the probability of an adverse outcome.
 Alternatively, it is a chance of financial loss or the variability of returns associated with an asset.
 A common measure of risk is the variance or SD of expected returns.

Use of standard deviation and variance in assessing risk: advantages
 Underlying intuition is that the greater the difference between actual payoff and expected value, the greater the risk.
 By squaring the difference and multiplying each difference by its associated probability then summing, this yields the variance of the possible outcome.
 Variance takes into account the number of potential outcomes or the probability of each outcome.
 It also provides a measure of risk that has a consistent interpretation across different situations or assets.
 Square root of variance gives standard deviation.

Interpreting the variance and standard deviation
 Var and SD especially useful measures of risk for variables that are normally distributed.
 Returns for many assets in finance tend to be approximately normally distributed.
 Standard deviation provides a convenient way of calculating the probability that the return on an asset will fall within a particular range.
 The expected return on an asset equals the mean of the distribution and the SD is a measure of the uncertainty associated with the return.

Standard deviation and variance calc
 Standard deviation= square root of variance
 Standard deviation calc: find the average returns (returns, sigma, down shift 7) then press shift down 8
 To find Variance: square SD

Normal distribution
 Normal distribution: a symmetric frequency distribution that is completely described by its mean and SD. AKA bell curve.1 SD= 68.26% of population
 1.645 SD= 90%
 1.96 SD= 95%

Risk measurement: coefficient variation
 If two investments with opposite return and risk, which would you choose?
 Coefficient variation: SD/E(r)
 is a ratio between SD and the return.
 Tells you for every 1% return, how much risk do you take?
 eg. 0.06/0.08= 0.75
 0.08/0.10= 0.8
 Choose the one with lowest number.

Difference risk attidues
 Risk neutral: a risk neutral investor is one who neither likes no dislikes risk. Whose utility is unaffected by risk.
 Such investors focus on expected return.
 Risk averse investor: one who demands compensation in the form of higher expected returns in order to be induced into taking more risk.
 Risk seeking investor: one who derives utility from being exposed to risk. May be willing to give up some expected return in order to be exposed to additional risk.

The riskreturn trade off
 Standard assumption in finance theory is that investors are 'risk averse'.
 Such investors regard risk ( or uncertainty) as undesirable and therefore require compensation for assuming risk in the form of an enhanced expected return.
 For such investors, there is a trade off between risk and expected return.

Risk premium
 The risk premium is the added return (over the risk free rate) resulting from bearing risk.
 Also called excess return.
 Eg. if current rate for one year treasury bill is 2%, what is the excess return on Apple's stock if it earns an average of 12.9%?
 =10.9%

Types of risk
 Firm specific: unsystematic risk. Affects only a specific company.
 It does not affect other firms
 Market risk: systematic risk. Affects the economy as a whole and therefore affects all shares.

Diversification
 Diversification: by investing intwo or more assets whose values do not always move in the same direction at the same time, investors can reduce the risk of the portfolio.
 The risk is diversified away in a portfolio is firm specific.
 Market risk is not diversifiable.

What is the risk premium for unsystematic/systematic risk?
 Unsystematic: zero. Should not be compensated for firm specific risk as can diversify.
 Systematic: positive because cannot diversify, affects everyone

