FINC341 chapter 8- risk

expected and required rates of return use the same process when dealing with

probability distribution

coefficient of variation (CV)

sigma/k hat = risk per unit of return

standard deviation (sigma), "measure of how far the actual return is likely to deviate from the expected return"

square root of the sum of all differences between each rate of return and expected rate of return (k hat) squared, multiplied by the probability for that rate of return

risk of an asset held by itself is called

stand-alone risk

the slope of the SML reflects

the degree of risk aversion in the economy- the greater the average investor's risk aversion - the steeper the slope of the line - the greater the risk premium for all stocks- hence the higher the required rate of return

stocks are less risky when held as part of a long-term portfolio

"the safest long-term investment for the preservation of purchasing power has clearly been stocks, not bonds."

implied beta for a stock

(practice problems)

expected rate of return (k hat)

(probability 1)(rate of return 1)+ (P2k2) + ... + (Pnkn) - weighted average of the expected returns in a portfolio

What are three potential problems with estimating the market risk premium?

1. What is the proper number of years over which to compute an average? 2. Historical premiums are likely to be misleading at times when the market risk premium is changing. 3. survivorship bias: historical estimates may be biased upward because they include only the returns of firms that have survived—they do not reflect the losses incurred on investments in failed firms.

Know these 3 numbers

68.3% represents +-1 sigma 95.5% represents +-2 sigma 99.7% represents +-3 sigma

tax shelter annuity (tsa)

A tax-sheltered annuity (TSA) plan is a retirement savings program authorized by section 403(b) of the Internal Revenue Code for employees of educational institutions, churches, and certain non-profit agencies. It allows eligible employees to set aside up to virtually 100% of their income for retirement.

diversifiable risk VS market risk (nondiversifiable)

EX: company-specific risk EX: pandemic

What does a 95.5% confidence interval really mean?

It means you are 95.5% confident the actual return is within 2 standard deviations of the expected return.

What's positive alpha? Negative alpha?

Once again, the SML shows the required returns for a given level of risk. Investments outperform the market when they earn realized returns that are greater than these required returns—doing so is often referred to as generating positive alpha. Similarly, investments with realized returns below their required returns have negative alphas. Graphically, positive alpha investments end up above the SML, whereas negative alpha investments end up below the SML.

Security Market Line equation

Required return on stock = risk free rate + (market risk premium)(stock i's beta) ki = krf + (Km-Krf)(bi)

Why do the standard deviations of individual stocks in a well-diversified portfolio no longer matter, and only beta of the portfolio matters?

Standard deviation is a measure of stand-alone risk- which is not useful in a portfolio with diversification. The risk of a stock in a portfolio, is typically lower than the risk of stand-alone asset. The portfolio's is NOT a weighted average in contrast to its expected return. The tendency of a stock to move with the market is its beta coefficient- it is calculated using historical data. The steeper the line, the greater its beta coefficient (the slopes of the lines are the stocks' beta coefficients). Thus, beta measures a given stock's volatility relative to the market.

What is the reasoning behind the SML equation (CAPM)

The Capital Asset Pricing Model is based off of the concept that a stock's required return should be equal to its risk free rate of return plus a risk premium that reflects only the risk after diversification.

Why is the correlation coefficient more important than the standard deviation

The correlation coefficient is a measure of risk per unit of return. Standard deviation is a measure of how much the actual return might deviate from the expected return. The correlation coefficient takes it a step further and compares standard deviation to expected return, in order to show risk per unit of return.

market risk premium

The market risk premium is a key component of the CAPM, and it should be the difference between the expected future return on the overall stock market and the expected future return on a riskless investment.

As the expected rate of inflation increases

a premium must be added to the real risk-free rate of return to compensate investors for the loss of purchasing power that results from inflation.

why do people invest in bonds

don't want risk, already have your nest egg, people are investing in bonds because rates are high and less risk

what is the difference between a stock's required return and its expected return

expected return is not the actual return, but an estimate of what the stock will return. Required return is calculated using the CAPM model and reflects what an investor should receive relative to the risk of said asset.

when working with the SML equation, why does a change in inflation affect both the nominal risk-free rate and the mkt return? Why does the slope NOT change when inflation changes?

inflation premiums are built into both Rf rate (IP) and market securities. the slope (beta) does not change because it is a measure of the riskiness of an asset COMPARED to the market (risk free)

Capital Asset Pricing Model (CAPM)

model based on the proposition that any stock's required rate of return is equal to the risk-free rate of return plus a risk premium that reflects only the risk remaining after diversification 1. calculate Required Ks (return on stock) 2. use in gordon model 3. calculate Po (Price)

why does a change in risk aversion affect the market return, but not the nominal risk-free rate of return?

the slope of the line represents the extent to which investors are risk averse (fear of the market). the steeper the slope, the more the average investor requires as compensation for bearing risk. No risk aversion means no risk premium- thus, the nominal risk-free rate of return is not affected.

which is riskier? a stock's return that has a high standard deviation or a low standard deviation?

the standard deviation represents the extent to which the actual return deviates from the expected return. A higher standard deviation is riskier. If standard deviation increases, the coefficient of variation increases, meaning the risk per unit of return increases.

The slope of the SML reflects the extent to which investors are averse to risk—

the steeper the slope of the line, the more the average investor requires as compensation for bearing risk.

beta coefficient

volatility, beta of average stock is 1.0