Financial Management: Chapter 6 - Risk, Return, & the Capital Markets

The rate of return that the investor should receive from owning one stock =

*Ri = Rrf + bi(RPM)* The return/risk of owning one stock = Risk free rate + Premium Premium = beta for the stock x market risk premium (for being in the market at all)

Returns can be expressed in 2 ways:

1. Dollar terms = $ Received - $ Invested 2. Percentage terms =$ Profit/$ Initial cost of investment

The CAPM: The Bottom Line (3)

1. Empirical tests of CAPM have statistical problems that make empirical verification or rejection virtually impossible. - Difficult to estimate share price or market behavior 2. Most corporations use the CAPM to determine their stock's required return. 3. Most researchers use multi-factor models to identify the portion of a stock's return that remains unexplained after accounting for the model's factors.

Calculating beta for a stock (3 steps)

1. Gather data on the stock's returns and the market returns (S&P 500) 2. Run a regression with: - Y-axis = returns on the stock - X-axis = returns on the market portfolio 3. The slope of the regression line is equal to the stock's beta coefficient

How is equilibrium established if market price is below the intrinsic value? (3 steps)

1. If the market price is below the intrinsic value (or if the expected return is above the required return), then the security is a "bargain." 2. So you'll start buying at the market, which will bid up the price to the intrinsic value orders - This also drives down the expected return, given no change in the asset's cash flows 3. "Profitable" trading (i.e., earning a return greater than justified by risk) will continue until the market price is equal to the intrinsic value.

How is equilibrium established if market price is above the intrinsic value? (3 steps)

1. If the market price is below the intrinsic value, then the security is a "" 2. So people who are opportunists will sell at the higher price, which will bid down the price to the intrinsic value orders - This also drives up the expected return, given no change in the asset's cash flows 3. "Selling short" will continue until the market price is equal to the intrinsic value.

Steps to CAPM for one stock (4)

1. If there is no risk in the stock, then Return of the market is the risk free rate Rm = Rrf - *Can't be true* cuz there's more risk in the market than a US treasury bill (Rrf)! 2. If the investor "buys the entire market", then they must be compensated for taking on more risk - Compensation = getting a Market Risk Premium (RPM) *Rm = Rrf + RPM (true!)* 3. If the investor buys only 1 stock, then what? - He/She must be further compensated for the risk of that one stock compared to the market. - That "compensation" or Risk Premium for the stock (RPi) is based on the volatility of that stock's return to the market (more variability, more risk, higher premium deserved), as measured by beta of the stock (bi) The risk premium we expect for owning one stock (RPi) = Beta (bi) x Market risk Premium (RPM) * 4. The rate of return that the investor should receive is a key useful CAPM insight: *Ri = Rrf + bi(RPM)*

Using the Required Rate of Return for evaluating stock portfolio managers (i.e. which one is better?) (2 steps)

1. Look at Portfolio returns, Portfolio betas, and Required rate of return 2. Find out if they're over or under-performing = Portfolio returns - Required rate of return = How much they're actually making - How much they should be making - Good result is if this difference is *positive*

Stock Market - steps in deciding which one of two stocks to buy

1. Overview - Graph the rates of return for the 2 stocks - Compute the average rate of return ("mean") - Compute the variability ("standard deviation") 2. Make Observations "so what"? - Which stock is more volatile? (look at standard deviation) - Higher standard deviation = more volatile 3. If the two projects move in tandem in opposite directions (e.g. one goes up, the other goes down), then there's the potential of portfolio diversification or improvement

Market bubbles (4)

1. Prices climb rapidly to heights that would have been considered extremely unlikely before the run-up. 2. Trading volume is unusually high. 3. Many new investors (or speculators?) eagerly enter the market. 4. And then Prices suddenly fall precipitously - bubble bursts!

2 ways to use Excel to calculate beta for a stock

1. Regression function 2. Shortcut—use the Excel SLOPE function. b =SLOPE(y_values,x_values) But you don't get all the statistics

2 exceptions with small excess returns to Weak-form EMH

1. Short-term momentum 2. Long-term reversals

2 exceptions that earn excess returns for Semi-Strong Form EMH

1. Small companies 2. Companies with high book-to-market ratios

Implications of the Efficient Market Hypothesis (EMH) (2)

1. Stocks are normally in equilibrium. 2. One can't "beat the market" by consistently earning a return higher than is justified by a stock's risk

The portfolio beta

= the weighted average of the stocks' betas bp = (w1b1 ) + ((w2b2) + (w3b3 ) +.... + (wn bn ) i.e. (weight of stock 1 x beta for stock 1) + ...etc. Can use the Security market line (SML) to find required rate of return on the portfolio

Strong-form EMH

All information, even inside information, is embedded in stock prices. Not true—it's illegal for excess returns to be gained by trading on the basis of insider information. - Go to jail now!

Risk vs. Number of Stocks in Portfolio i.e. What happens to portfolio risk when you add more stocks to it that have some diversification characteristics?

As we add more stocks that have some diversification characteristics, we can decrease total portfolio risk - But each new stock has a smaller risk-reducing impact on the portfolio. As you add more stocks, you'll approach but not completely reach the market risk cuz you're not having the entire market risk go away Standard deviation (of p) falls very slowly after about 40 stocks are included - not a lot of diversification remaining after 40 - The lower limit for Standard deviation (of p) is about 20% = Standard deviation (of M).

If two portfolio investments are equally risky (i.e. rate of returns are identical), how can you reduce risk? i.e. What is the value of diversification to reduce risk?

Buy 50% of each portfolio! The return is the average of the two, and the risk would be zero (no variation)! - kinda like noise cancellation

What's the benefit to investors of forming well-diversified portfolios?

By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock.

Capital Asset Pricing Model (CAPM)

CAPM is a well accepted method that quantifies the risk-return relationships (tradeoffs) of the market, individual stocks, and portfolios of stocks

Which risk can be diversified and lowered: company or market?

Company risk can be diversified and lowered, but not market risk

Semistrong-form EMH

Current prices already reflect all publicly available information, so analyzing a company is futile because it's already been factored in. Example strategy: Invest in stocks with past 5-year annual earnings growth greater than 10%. This is a type of "fundamental" analysis. We do a full analysis - look at the past, all the information, and we interpret what that might mean for the future

Weak-form EMH

Current prices already reflect all the information "contained" in *past prices* - So we can look at historical patterns of the price - see how it moves up/down, look at tendencies - This is a type of "technical" analysis. Example strategy: Invest in stocks that have declined below their previous 52-week low. It's kind of backward looking, looks at that to find some opportunities in the current pricing -BUT you can't earn excess returns with strategies based on past prices.

Evidence to support Semi-Strong Form EMH

Empirical evidence supports the semi strong-form EMH. - In fact, the vast majority of portfolio managers do not consistently have returns in excess of CAPM predictions

Evidence supporting the Weak From

Empirical evidence supports weak-form EMH because very few trading strategies consistently earn in excess of the CAPM prediction. There are a few strategies where you can earn a little extra return - that's why there are automatic trading platforms to take advantage of these small anomalies in the price of stocks

Compute the expected return (based on history):

Excel function "SumProduct" *= sumproduct (range of probabilities, range of returns)* Expected Rate of Return = puts together the expected outcomes in rates of return, and weights it based on the probability of the occurrence Multiply the different probability with outcomes, and then add them together

What is investment risk?

Exposure to the chance of earning less than expected. The greater the chance of a return far below the expected return, the greater the risk We look at all the scenarios possible for the outcomes of this investment, assign probabilities to each scenario, and see the returns for those scenarios

What's the key result from CAPM?

Finds the *required return on equity!*

Market Efficiency: The Bottom Line

For most stocks, for most of the time, it is generally safe to assume that the market is reasonably efficient and the prices are reasonably set. Many investors have given up trying to beat the market, so they buy diversified portfolios instead. - which helps explain the popularity of index funds (constructed to exactly mirror the S&P 500) - S&P 500 prices will always rise in the long run However, bubbles do occur infrequently.

If the Risk Free Rate increases, what is the impact on SML?

If market conditions increase the cost of US Treasury Bills, and if there are no changes in market risk premium, then *Required return for all stocks increases by the same amount* i.e. SML line shifts up - Premium stays the same, so slope stays the same - Only y-intercept (rate of return) changes (higher)

What does Market Bubbles imply about the EMH? (2)

If there is a bubble, why don't traders take positions that make big profits when the bubble bursts? - It is hard to recognize a bubble until after it bursts—cuz everyone is believing the same set of information - Trading strategies expose traders to possible big negative cash flows if the bubble is slow to burst.

Steps to CAPM for Portfolio of stocks (3)

If this works for one stock, then it can be generalized to the portfolio based on the weights (percentages) of each stock in the portfolio: a. The portfolio standard deviation σp = (w1σM b1 ) + (w2σM b2) + (w3σM b3 ) +.... + (wnσM bn) i.e. weighting of stock 1 in the portfolio x standard deviation of the market x beta for stock 1 ...continue b. The portfolio beta bp = (w1b1 ) + ((w2b2) + (w3b3 ) +.... + (wn bn ) i.e. weight of stock 1 x beta for stock 1 c. And, finally, the *portfolio expected return* Rp= Rrf + bp (RPM) = Risk free rate of market + (beta of portfolio x market risk premium in general)

Standard Deviation

Measure of "stand-alone risk" of a single asset i.e. the dispersion of possible outcomes around the expected value Higher S.D. = Higher Variation = Higher Risk

What are investment returns?

Measures the financial results of an investment Returns may be historical or prospective (anticipated)

If the Market becomes more Risk Averse, what is the impact on SML?

Need a higher market risk premium for taking on more risk i.e. Slope becomes more steep

Has the CAPM been completely confirmed or refuted? (3)

No. - The statistical tests have problems that make empirical verification or rejection virtually impossible. - Investors' required returns are based on future risk, but betas are calculated with historical data. - Investors may be concerned about both stand-alone and market risk.

The Correlation Coefficient (ρi,j)

Pronounced "rho". Helps us predict the degree to which the 2 stocks act to have this "noise cancelling" effect i.e. Measures the tendency (correlation coefficient) of two variables (rate of return of both projects) to move together. Estimating ρi,j with historical data is tedious, so we use: Excel = *Correl(Range of rate of returns for Stocki, Range of rate of returns for Stockj)*

Risk formula

Risk = Market Risk + Company Specific Risk So gap between market risk and risk of the portfolio = company specific (diversifiable) risk

Probability distributions for investments: which shapes show that a riskier investment?

Risk is measured by the variance i.e. the amount of variation away from the mean The greater the variation, the higher the risk Low risk = narrower distributions i.e. variance is closer to the mean High risk = wider distributions i.e. variance extends further from the mean Both risks have identical expected values (mean), but have different distributions

2 types of standard deviations on Excel

Standard deviation, *population = stdev.p(range of returns)* --> gets std of entire population, full results - Use if the population is known Standard deviation, *sample = stdev.s(range of returns)* --> gets std of a sample population, results that you generalize from - Can find possible loss of profit = Mean of range of returns - Std of range of returns i.e. -1 standard deviation - Can find possible gain in profit = Mean of range of returns + Std of range of returns i.e. +1 standard deviation

Efficient Market Hypothesis (EMH) (3)

The Price of a Stock Considers All Information (that is known) Guesses whether you believe that the market price is correct or not The EMH asserts that when new information arrives, prices move to the new equilibrium price very, very quickly because: 1. There are many really *smart analysts looking for mispriced securities.* 2. New information is available to most professional traders almost instantly. 3. When mispricing occurs (due to new info or inefficient markets), analysts have billions of dollars to use in taking advantage of the mispricing- which then *quickly eliminates the mispricing.*

Comparing Risk and Return for Different Stocks with different betas

The beta of an average stock is 1.0 (by definition) - i.e. it moves with the market Beta over 1 = more volatile stock - Would have a higher rate of return than market Beta under 1 = more stable stock - Would have a lower rate of return than market Most stocks have betas in the range of 0.5 to 1.5. When we blend portfolios, we pick up some diff portfolio characteristics, given the relative return and the beta of the different stock options

What is required for the market to be in equilibrium?

The market price of a security must equal the security's intrinsic value (intrinsic value reflects the size, timing, and risk of the future cash flows). *Market price = Intrinsic value* The expected return of a security must equal its required return (which reflects the security's risk). 𝐫 = r

How to interpret Correlations for Stock Portfolios (3)

p = −1 (perfect negative correlation) = one goes up the other goes down by the same amount - 2 stocks can be combined to form a riskless portfolio: σp = 0. p = +1 (perfectly correlated, move lock step with each other) - Risk is not "reduced" - no diversification benefit by mixing the two cuz they just move together anyways - σp is just the weighted average of the 2 stocks' standard deviations. −1 < p < +1 - Risk is reduced but not eliminated.

The Security Market Line (SML)

ri = rRF + (RPM)bi Shows the market risk-return relationship. Slope of line (require rate of return) is determined by market risk premium

Stand-alone risk

the risk of each asset held by itself.