Risk & Return

SML slope

(E(R of M) - Rf)/Beta of M = (E(R of M) - Rf)/1 = (E(R of M) - Rf)

Portfolio

a group of assets such as stocks and bonds held by an investor

diversifiable risk

risk that can be eliminated by diversification

total risk

systematic risk + unsystematic risk

Capital Asset Pricing Model (CAPM)

the equation of the SML showing the relationship between expected return and beta

in an active, competitive market...

(E(R of B) - Rf)/beta of B. The reward-to-risk ratio must be the same for all the assets in the market, they all must plot on the same line if an asset is plotted above the line, its price would rise, and its expected return would fall until it plotted exactly on the line. similarly, if an asset is plotted below the line, its price would fall, and its expected return would rise until it plotted exactly on the line

what does he security market line tell us?

- The reward for bearing risk in financial markets. At an absolute minimum, any new investment our firm undertakes must offer an expected return that is no worse than what the financial markets offer for the same risk. The reason for this is that our shareholders always can invest for themselves in the financial markets. - The only way we benefit our shareholders is by finding investments with expected returns that are superior to what the financial markets offer for the same risk. Such an investment will have a positive NPV. So, if we ask: "What is the appropriate discount rate?" the answer is that we should use the expected return offered in financial markets on investments with the same systematic risk. - In other words, to determine whether or not an investment has a positive NPV, we essentially compare the expected return on that new investment to what the financial market offers on an investment with the same beta. This is why the SML is so important; it tells us the "going rate" for bearing risk in the economy.

Expected and Unexpected Returns

- To begin, for concreteness, we consider the return on the stock of a company called Flyers. What will determine this stock's return in, say, the coming year? - The return on any stock traded in a financial market is composed of two parts. First, the normal, or expected, return from the stock is the part of the return that shareholders in the market predict or expect. This return depends on the information shareholders have that bears on the stock, and it is based on the market's understanding today of the important factors that will influence the stock in the coming year. - The second part of the return on the stock is the uncertain, or risky, part. This is the portion that comes from unexpected information revealed within the year. A list of all possible sources of such information would be endless, but hem are a few examples: • News about research on Flyers. • Government figures released on gross domestic product (GDP). • The results from the latest arms control talks. • The news that Flyers's sales figures are higher than expected. • A sudden, unexpected drop in interest rates. Based on this discussion, one way to express the return on Flyers's stock in the coming year would be: Total return = Expected return + Unexpected return R = E(R) + U - where R stands for the actual total return in the year, E(R) stands for the expected part of the return, and U stands for the unexpected part of the return. What this says is that the actual return, R, differs from the expected return, E(R), because of surprises that occur during the year. In any given year, the unexpected return will be positive or negative, but, through time, the average value of U will be zero. This means that, on average, the actual return equals the expected return.

A risk free asset has a beta of...

0

Unsystematic risk

A risk that affects at most a small number of assets. Also, unique or asset-specific risk

Systematic risk

A risk that influences a large number of assets. Also, market risk.

Risk-free investment

If we always receive exactly what we expect, then the investment is perfectly predictable and, by definition, risk-free

Total return = Expected return + Unexpected return (R = E(R) + U ) can be broken down into...

R = E(R) + m + ε, where m is the systematic portion of surprise, and ε is the unsystematic portion of surprise

Relationship between portfolio size and portfolio risk

Standard deviation declines as the number of securities is increased

What does the CAPM show us?

That expected return for a particular asset depends on three things: 1. The pure time value of money. As measured by the risk-free rate, Rf, this the reward for merely waiting for your money, without taking any risk. 2. The reward for bearing systematic risk. As measured by the market risk premium, [E(R of M) - Rf], this component is the reward the market offers for bearing an average amount of systematic risk in addition to waiting. 3. The amount of systematic risk. As measured by βi this is the amount of systematic risk present in a particular asset, relative to an average asset. By the way, the CAPM works for portfolios of assets just as it does for individual assets. In an earlier section, we saw how to calculate a portfolio's β. To find the expected return on a portfolio, we use this β in the CAPM equation.

What is the appropriate discount rate on a new project?

The minimum expected rate of return an investment must offer to be attractive/ This minimum required return often is called the cost of capital associated with an investment

What's the true risk of any investment?

The unanticipated part of return, that portion resulting from surprises, is the true risk of any investment

We say an investment is attractive since its expected return exceeds what is offered in the financial markets for investments of the same risk, we are effectively using the IRR, criterion. What's the only difference now?

We have a much better idea of what determines the required return on an investment

Announcements & News

We need to be careful when we talk about the effect of news items on the return. For example, suppose Flyers's business is such that the company prospers when GDP grows at a relatively high rate and suffers when GDP is relatively stagnant. In this case, in deciding what return to expect this year from owning stock in Flyers, shareholders either implicitly or explicitly must think about what GDP is likely to be for the year. When the government actually announces GDP figures for the year, what will happen to the value of Flyers's stock? Obviously, the answer depends on what figure is released. More to the point, however, the impact depends on how much of that figure is new information. At the beginning of the year, market participants will have some idea or forecast of what the yearly GDP will be. To the extent that shareholders have predicted GDP, that prediction already will be factored into the expected part of the return on the stock, E(R). On the other hand, if the announced GDP is a surprise, then the effect will be part of U, the unanticipated portion of the return. Suppose shareholders in the market had forecast that the GDP increase this year would be .5 percent. If the actual announcement this year is exactly .5 percent, the same as the forecast, then the shareholders don't really learn anything, and the announcement isn't news. There will be no impact on the stock price as a result. This is like receiving confirmation of something that you suspected all along; it doesn't reveal anything new. A common way of saying that an announcement isn't news is to say that the market has already "discounted" the announcement. The use of the word discount here is different from the use of the term in computing present values, but the spirit is the same. When we discount a dollar in the future, we say it is worth less to us because of the time value of money. When we say that we discount an announcement, or a news item, we mean that it has less of an impact on the market because the market already knew much of it. For example, going back to Flyers, suppose the government announces that the actual GDP increase during the year has been 1.5 percent. Now shareholders have learned something, namely, that the increase is one percentage point higher than they had forecast. This difference between the actual result and the forecast, one percentage point in this example, is sometimes called the innovation or the surprise. An announcement, then, can be broken into two parts, the anticipated, or expected, part and the surprise, or innovation: Announcement = Expected part + Surprise The expected part of any announcement is the part of the information that the market uses to form the expectation, E(R), of the return on the stock. The surprise is the news that influences the unanticipated return on the stock, U. To take another example, if shareholders knew in January that the president of the firm was going to resign, the official announcement in February would be fully expected and would be discounted by the market. Because the announcement was expected before February, its influence on the stock would have taken place before February. The announcement itself will contain no surprise, and the stock's price shouldn't change at all when it is actually made. The fact that only the unexpected, or surprise, part of an announcement matters explains why two companies can make similar announcements but experience different stock price reactions. For example, to open the chapter, we compared Hormel, Microsoft, and Okta. In Hormel's case, even though the company's earnings had grown about 13 percent to $A4 per share, analysts' estimates for the stock pegged EPS at $.45, so the company came in below expectations. In Microsoft's case, even though the company had exceeded analysts' estimates, the company was trading at high valuations, with high PE and EV/EBITDA multiples, so the earnings "beat" was not enough to impress investors, who were expecting even better numbers. And while Okta reported a loss for the quarter, the loss was only $.09 per share, much better than the expected $.16 per share. Our discussion of market efficiency in the previous chapter bears on this discussion. We are assuming that relevant information known today is already reflected in the expected return. This is identical to saying that the current price reflects relevant publicly available information. We are thus implicitly assuming that markets are at least reasonably efficient in the semistrong form sense. Henceforth, when we speak of news, we will mean the surprise part of an announcement and not the portion that the market has expected and therefore already discounted.

Is it possible for the percentage invested in an asset to exceed 100%?

Yes, if the investor were to borrow at the risk-free rate. Suppose an investor has £100, and borrows an additional £50 at 8%, the risk-free rate. The total investment in the asset would be £150, or 150% of the investor's wealth.

assets with larger betas have greater systematic risks, therefore, they will have...

greater expected returns e.g. an investor who buys stock in ford, with a beta of 0.85, should expect to earn less, on average, than an investor who buys stock in apple, with a beta of 1.15.

when is an asset said to be overvalued?

if its price is too high given its expected return and risk

market portfolio

portfolio made up of all assets in the market expected return no this market portfolio is E(R of M)

Principle of diversification

spreading an investment across a number of assets will eliminate some, but not all, of the risk

diversification & systematic risk

systematic risk cannot be eliminated through diversification because systematic risk affects almost all assets to some degree. systematic risk & non-diversifiable risk/market risk are used interchangeably

beta coefficient

the amount of systematic risk present in a particular risky asset relative to that in an average risky asset. we use this to measure the level of systematic risk for different investments by definition, an average asset has a beta of 1.0 relative to itself. an asset with a beta of 0.50, therefore has half as much systematic risk as an average asset; an asset with a beta of 2.0 has twice as much

alpha

the excess return an asset earns based on the level of risk taken

systematic risk principle

the expected return on a risky asset depends only on that asset's systematic risk

Risk/Reward Ratio

the greater the risk, the greater the potential reward slope of the line is the risk premium of the asset i.e. (E(R of A) - Rf)/beta of A. this slope value offers a reward-to-risk ratio of x%. in other words, the asset has a risk premium of x% per "unit" of systematic risk If the line describing the combinations of expected returns and betas for a second asset is higher than the one for the first asset, this tells us that for any given level of systematic risk (as measured by beta), some combination of the second asset and the risk-free assets always offers a larger return, therefore, the second asset is a better investment than the first asset also, if the reward-to-risk ratio for one asset is higher than the other, this means that it offers a superior return for its level of risk

nondiversifiable risk

the minimum level of risk that cannot be eliminated simply by diversifying

Portfolio weights

the percentage of a portfolio's total value that is invested in a particular asset E.g., if we have $50 in one asset and $150 in another, then our total portfolio is worth $200. The percentage of our portfolio in the first asset is $50/$200 = 25%. The percentage of our portfolio in the second asset is $150/$200 = 75%. 25% + 75% = 100% because all of our money is invested somewhere

market risk premium

the slope of the SML - the difference between the expected return on a market portfolio and the risk-free rate E(R of M) - Rf

diversification & unsystematic risk

unsystematic risk is essentially eliminated through diversification, so a relatively large portfolio has almost no unsystematic risk the terms diversifiable/unique/asset-specific risk and unsystematic risk are often used interchangeably