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Finance 380 Midterm Note

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Lecture 1 -­‐ Arithmetic Average 1. Ignores compounding; 2. Does not represent an equivalent, single quarterly rate for the year; 3. Is the best forecast of performance for the next quarter without information beyond the historical sample. -­‐ Geometric Average 1. Also called a time-­‐weighted average return-­‐ignoring the quarter-­‐to-­‐quarter variation in funds under management; 2. Mutual funds are required to publish this as a measure of past performance. -­‐ Dollar-­‐weight Return 1. Similar to a capital budget problem 2. Accounting for varying amounts of capital under management form quarter to quarter 3. Less than time-­‐weighted return of 7.19% -­‐ Risk free assets: an asset with a certain rate of return (often taken to be short term T-­‐bills) -­‐ Scenario analysis: l Determine a set of relevant scenarios and associated investment outcomes and assigns probability to each l l -­‐ Compute mean return and variance However, sometimes it is hard to assign probabilities

Time series analysis: l l Use historical data, treat each observation as equally likely Compute mean and variance

-­‐ -­‐

Normal distribution, ri~N(E(ri), Oi) Two special properties:

l

The return on a portfolio comprising two or more assets whose returns are normally distributed also will be normally distributed.

l

The normal distribution is completely described by its mean and standard deviation.

Lecture 2 -­‐ Preference: risk aversion (not inconsistent) Investors will avoid risk unless there is a reward Sometimes this assumption may be violated People gamble More interestingly, people both gamble and buy insurance -­‐ Speculation (not inconsistent) The assumption of considerable investment risk to obtain commensurate gain considerable risk: risk sufficient to affect the decision Commensurate gain: positive risk premium -­‐ risk averse investors consider only risk free or speculative assets with positive risk premiums -­‐ gamble (irrational): to bet or wager on an uncertain outcome; assuming risk for no purpose but enjoyment of the risk itself. -­‐ Capital allocation across risky and risk-­‐free assets: investors can construct portfolios by allocation capital across different asset classes; the most basic asset allocation choice: choose the fraction of the portfolio invested in risk-­‐free assets versus the portion invested in the risky asset; consequence: different risk and return trade-­‐off -­‐ Risk-­‐free asset: only the government can issue default-­‐free bonds. (only if price indexed and maturity equal to investor’s holding period) -­‐ Levered complete portfolios: this are portfolios to the right of P on the CAL: y>1; borrow a proportion of y-­‐1 at the risk-­‐free rate and invest all funds into P. y = (own capital + borrowed capital)/ own capital -­‐ When do we have only on risky asset? Passive strategy: indexing. Buying a well-­‐diversified portfolio to represent a broad-­‐based market index without attempting to search out mispriced

securities. Rationale: 1. Efficient market: intense competition among professional money managers forces security prices to be fairly efficient. 2. Low cost. 3. Easy to implement -­‐ Passive strategies: the capital market line (CML) is the CAL formed by combining 1-­‐month T-­‐bill and a broad index of common stocks

Lecture 3 -­‐ Diversification and portfolio risk Consider a portfolio with only one stock A naïve diversification strategy with two stocks -­‐ Limits of diversification Market/systematic risk: risk factor common to the whole economy; non-­‐diversifiable Firm-­‐specific/non-­‐systematic risk: Diversifiable risk; risk that can be eliminated through diversification On average, portfolio risk falls with diversification; buy the power of diversification is limited by systematic risk. -­‐ Efficient Diversification: To achieve the lowest possible risk for any given level of expected return A key determinant of portfolio risk: covariance between asset returns Covariance measures the extent to which the returns on any two assets vary in either tandem or in opposition. -­‐ Covariance and portfolio risk: The portfolio standard deviation is actually smaller than that of either component fund. This is due to the inverse relationship between the performances of stock fund and bond fund. Mild recession: Poor stock return offset by positive bond return Boom: poor bond return offset by positive stock return -­‐ Correlation coefficient range from -­‐1 to +1 When p = 1 there is no diversification due to perfect positive correlation When p = -­‐1, a perfect hedge is possible due to perfect negative correlation When p

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