- 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 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: 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 risk-return 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.
- 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%?
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: 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