Topic 8: Diversification and Risk Decomposition

How does the slope of a regression line affect everything? What is the slope called and what does it indicate/measure?

- Steeper slope corresponds with larger systematic return variations - Slope of the regression line= beta coefficient or beta -Indicates how sensitive a stock is to systematic risks -A measure of systematic risk exposure

Systematic Risk Principle

- There is a reward for bearing risk - There is no reward for bearing risk unnecessarily The EXPECTED RETURN on a risky asset depends only ON THAT ASSET'S SYSTEMATIC RISK -Why? Because unsystematic risk can be diversified away at no most -Mutual funds (often with minimal initial investment) are widely available to investors -No matter how much total risk an asset has, its expected return depends only on its systematic risk

What is stock systematic risk?

-Systematic risk of an individual stock is how much risk it adds to a diversified portfolio -Risk of a diversified portfolio is the sum of all the elements in the "row" of the matrix -Each stock's contribution is the sum of its "row" of the matrix -Its "row" has 1 variance and N-1 covariances. Covariance is what matters!!!

Two ways to measure amount of total risk that is non-diversifiable or systematic?

1.Measure how much risk the stock adds to the market portfolio- this is driven by the stock's average covariance with the other assets in the market portfolio 2. Measure how much of the stock's total risk can be explained by the variance of the market portfolio-- this is done by regressing the stock returns against the market portfolio returns. The regression R^2 is the percentage of total risk that is non-diversifiable

Alpha In our discussion of the SML, we defined alpha. What does alpha measure? What alpha would you like to see on your investments?

Alpha measures the vertical distance of an asset's return from the SML. As such, it measures the return in excess of the return the asset should have earned based on the level of risk as measured by beta. A positive alpha means that the return is higher than it should have been given the level of risk taken, while a negative alpha means that the return was too low given the level of risk taken. Therefore, a positive alpha is always better. In an efficient market, we would expect that all assets would have an alpha of zero.

How are assets labeled when they are under or over the SML line?

Assets that plot above the SML are underpriced and offer an above equilibrium reward-to-risk ratio -There should be buying pressure on these assets, raising the price and lowering the expected return, pushing them toward the SML Assets that plot below the SML are overpriced and offer a below equilibrium reward to risk ratio -There should be seeling pressure on these assets, lowering the price and raising the expected return, pushing them toward the SML

Market portfolio and reward to risk ratio

Because the market portfolio has no idiosyncratic risk, it has the highest reward to total risk ratio - the market portfolio offers the highest sharpe ratio among all traded assets

How to interpret beta

Beta measures the relative amount of systematic risk present in an asset -The market has beta=1, and this is the average amount of systematic risk exposure for individual securities

Portfolio Betas

Beta of a portfolio is simply the weighted average of the betas of its securities:

Priced Risk

Communicates the crucial idea that non-diversifiable risk earns a higher expected return -Factor-->Rewarded via a Risk premium Risk--> Not rewarded: earns no risk premium

What form of risk is avoidable?

Diversifiable Non-diversifiable IS NOT - No investor needs to be exposed to non systematic risk because it can easily and cheaply be eliminated by holding a diverse portfolio of assets -This is the primary justification and benefit of index funds and the broad recommendation that non-professional investors are best off investing (for retirement, etc.) via index funds.

What are the different iterations of diversifiable risk and what is it?

Diversifiable/Idiosynchratic/Non systematic risks =risks that are unique to a small set of securities

What does a large portfolio infer?

Diversification, not size!

Risk-adjusted discount rates

E(return)=Risk free rate + risk premium Risk-free rate- compensation for TVM Risk premium- compensation for risk, will scale with the risk

Earnings and Stock Returns As indicated by a number of examples in this chapter, earnings announcements by companies are closely followed by, and frequently result in, share price revisions. Two issues should come to mind. First, earnings announcements concern past periods. If the market values stocks based on expectations of the future, why are numbers summarizing past performance relevant? Second, these announcements concern accounting earnings. Going back to Chapter 2, such earnings may have little to do with cash flow—so, again, why are they relevant?

Earnings contain information about recent sales and costs. This information is useful for projecting future growth rates and cash flows. Thus, unexpectedly low earnings often lead market participants to reduce estimates of future growth rates and cash flows; price drops are the result. The reverse is often true for unexpectedly high earnings.

Diversification True or false: The most important characteristic in determining the expected return of a well-diversified portfolio is the variance of the individual assets in the portfolio. Explain.

False. The variance of the individual assets is a measure of the total risk. The variance on a well- diversified portfolio is a function of systematic risk only.

What are securities referred to as?

For simplicity, we refer to all securities as stocks -The proportion of each stock in it is equal to the stock's market cap divided by the total market cap

What would having a large class of assets with negative beta mean?

Having large class of assets with negative beta would essentially mean that we're reversing market fluctuations of the whole market

How does covariance effect overall portfolio risk?

High covariance (with other assets) INCREASES overall portfolio risk Low covariance (with other assets) DECREASES overall portfolio risk

What is a market portfolio?

In theory, the most well diversified portfolio one could have: -Fully diversified -All idiosyncratic risk eliminated -Only nondiversifiable risk remains

What does increasing the number of stocks do to beta?

Increasing the number of stocks within the portfolio brings beta to 1 (makes it more diversifiable)

The term structure of risk-free rate generally increases with maturity, because of _____ and _______.

Inflation and interest rate risk -Government short-term rates (on T-bills): better proxy of "risk free" rates, as freer of default, interest, and inflation risk -T-Bonds are also sometimes used in practice to account for longer investment horizons

alpha Common advice on Wall Street is "Keep your alpha high and your beta low." Why?"

Keeping your beta low means that you have a low level of systematic risk, while a high alpha means that your return is high compared to the level of risk taken.

What does low beta imply in regards to systematic risk?

Low beta implies low systematic risk -Only systematic risk is priced by financial markets, because it is non-diversifiable -Securities with lower beta have lower systematic risk, hence lower expected returns

SML is a representation of what?

Market equilibrium -slope of sml= market risk premium

Does diversification have an impact on systematic risk exposure?

NO

Expected Portfolio Returns If a portfolio has a positive investment in every asset, can the expected return on the portfolio be greater than that on every asset in the portfolio? Can it be less than that on every asset in the portfolio? If you answer yes to one or both of these questions, give an example to support your answe

No to both questions. The portfolio expected return is a weighted average of the asset returns, so it must be less than the largest asset return and greater than the smallest asset return.

Are stocks with negative beta common? Why?

No, a negative side implies that it moves in the opposite direction of the market - Some stocks are negative in the short run, pretty much zero correlation with the market and slightly negative -Why are they not common? If they were we could perfectly hedge the market fluctuations and we wouldn't be having the discussion about systematic risk -Important because you could perfectly hedge yourself against systematic risk and you would require compensation

What type of risk is rewarded with extra return?

Nondiversifiable risk

What does diversification do to risk?

Only reduces/eliminates idiosyncratic risk

The CAPM states that the expected return for any asset or portfolio j depends on what three factors?

Pure time value of money= Rf -Compensation for having to wait for your money, regardless of risk Amount of Systematic Risk = βj -Relative to the amount in an average asset (market) Reward for Bearing Systematic Risk = E(RM) - RF -Market risk premium to compensate for bearing average (market) amount of systematic risk

Systematic v Unsystematic risk

Systematic risk: affects many stocks, like financial crisis Unsystematic: affects only one or two stocks, like lawsuit against a company

What is the correct cost of capital to use when evaluating an asset or project?

The correct cost of capital is the required return based on the systematic risk exposure of the asset or project

What does covariance show?

The degree that two stocks move together or apart is captured by the covariance between the returns of each stock

Market risk premium

The estimated average market risk premium is NOT the expected market risk premium for any particular future period ... but it is a reasonable guess Financial economists, analysts and companies come-up or rely on some estimates of equity risk premiums

What happens to risk premium when risk higher?

The higher the risk, the higher the risk premium Which risk? Only systematic risk is priced! The higher the beta, the greater the risk premium

What does the market portfolio include?

The market portfolio includes all financial securities -Stocks, government, and corporate bonds, mortgage-backed securities, etc.

Risk-to-reward ratio

The reward-to-risk ratio is the slope of the line

How are investors induced to bear non diversifiable risk

To induce investors to bear non diversifiable risk and reward them for doin

Underpriced assets offer ____ returns?

Underpriced assets offer (overly) high returns -Investors will seek to buy underpriced assets, hence bidding up their price and lowering their expected return -This process should continue until the asset return is lowered enough for the security to line up on the SML

What is the SP500 used for?

Used as a proxy for the "market" portfolio

What measures total risk? What does r-squared and beta tell us?

Variance or standard deviation -R-squared tells us the percentage of the total risk that is systematic risk -Beta tells us the amount of systematic risk exposure the asset has (relative to the average amount) A stock can have high total risk (i.e., a large variance) and low systematic risk (i.e., a low beta)

How do we measure systematic risk?

We measure it by estimating the sensitivity of a security's return to the market return -There is no idiosyncratic risk in market portfolio -That sensitivity is called BETA coefficient (β) OR how much your stock follows the market

Portfolio Risk If a portfolio has a positive investment in every asset, can the standard deviation on the portfolio be less than that on every asset in the portfolio? What about the portfolio beta?

Yes, the standard deviation can be less than that of every asset in the portfolio. However, bp cannot be less than the smallest beta because bp is a weighted average of the individual asset betas.

Beta and CAPM Is it possible that a risky asset could have a beta of zero? Explain. Based on the CAPM, what is the expected return on such an asset? Is it possible that a risky asset could have a negative beta? What does the CAPM predict about the expected return on such an asset? Can you give an explanation for your answer

Yes. It is possible, in theory, to construct a zero beta portfolio of risky assets whose return would be equal to the risk-free rate. It is also possible to have a negative beta; the return would be less than the risk-free rate. A negative beta asset would carry a negative risk premium because of its value as a diversification instrument.

Portfolio

a combination of assets defined by portfolio weights

Idiosyncratic risk

a function of how much the realized return deviate from the regression line

What is total risk?

a function of how much the realized returns deviate from the mean

What is systematic risk?

a function of how much the regression line deviates from the mean

Portfolio variance main takeaway

the overall portfolio risk is almost completely driven by how much (or little) the returns of the portfolio stocks covary with one another, and almost not at all by how individually risky a stock is. An individual stock that is very risky, but uncorrelated with all the other stocks, will contribute virtually nothing to the riskiness of the overall portfolio.

Portfolio Weights

the percentage of the total investment that is invested in each asset

The market risk premium and the intercept of the SML both depend on _________?

the risk-free rate RF - Interest rates are different for different horizons (term structure of interest rates) - which one should we use?

Risky assets v risk-free assets

By varying the weight wj, we can get an idea of the relationship between portfolio expected returns and betas