BUS202 Study Guide

Unit 5: Risk, Return, and the CAPM

5a. Explain the relationship between risk and reward

What is risk?
What is a reward or return?
What is the relationship between risk and return?
What types of risk are there?

Every financial transaction has an element of risk, meaning an investor can make or lose money on the transaction. The gain an investor makes on a transaction is called a reward or return. Risk is the uncertainty of future cash flows. There are many types of risk, such as liquidity risk, operational risk, market risk, price risk, credit risk, counterparty risk, maturity risk, default risk, geopolitical risk, and many more. For every risk, there is an accompanying risk premium. The types of risk are derived from the understanding that elements or events could jeopardize the expected cash flows from a transaction. In finance, the common saying is, "The greater the risk, the greater the expected reward".

Return is the reward one gets for bearing risk. The riskier a transaction, the greater the payout you should expect. Sometimes investors want to maximize the return portion of an investment portfolio while minimizing the risk. To achieve that, there are primarily three options for risk mitigation: diversification, hedging, and purchasing insurance of some type. Purchasing insurance on a financial position or investment is pretty straightforward to understand. Hedging requires the investors to take an opposite and offsetting position.

Since there is a chance that an investor may not profit from a transaction, investors can compute an expected return. The expected return is the total return anticipated after considering both the expected payout and the likelihood of that payout occurring. To compute the expected value of one investment, multiply the investment's expected payout (profit or loss) times the probability that that payout will occur. This technique can be used to compare the expected value of investments so that you can determine how to best allocate funds, or it can be done for a group of investments (known as a portfolio) that the investor has simultaneously invested in to determine the total expected return of all investments held.

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5b. Compute expected values when risk issues need to be considered in finance

What does "expected value" mean in the context of finance?
How do you calculate the expected value of an investment?
What is probability?

In finance, the expected value represents the average outcome of an uncertain event, weighted by the probabilities of all possible outcomes. It helps investors and managers make rational decisions under risk or uncertainty. It provides a quantitative measure of what an investment or decision is worth on average over time. It helps compare alternatives in risk-based financial decisions (investments, project selection, insurance). It's a core concept in probability, portfolio theory, and capital budgeting.

The expected value is calculated using the weighted average of all possible outcomes. We can calculate the expected return for an investment by multiplying the potential return by the probability that each scenario will occur and summing each product.

Probability is the likelihood that an event or scenario will occur. For example, a weather forecaster may judge that there is a 40% chance of rain based on their analysis of weather patterns. Likewise, an investor may foresee a 30% probability of a bear market and a 70% probability of a bull market. Probabilities must add up to 100%: all scenarios must be considered.

Since these scenarios are not certain, they contain an element of risk. Investors may estimate the likelihood of how much return they will achieve across a range of possible economic scenarios. The expected return is found by multiplying the probability of each scenario by the return that will be earned if that scenario occurs. Each product is added to find the overall expected return, the weighted average of the various possibilities.

Here is the formula to calculate the expected return:

E[R]= (Probability_a)×(Return_a)+(Probability_b)×(Return_b)+(Probability_c)×(Return_c) + …..

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5c. Compare systematic and unsystematic risk

What is the difference between systematic and unsystematic risk?
How do systematic and unsystematic risks affect an investor differently?
Can investors diversify away all risk?

We can classify investment risk as systematic or unsystematic (specific) risk. Systematic risk is the risk associated with the overall market. Factors such as economic conditions and political events impact the entire market. Systematic risk cannot be diversified away by holding multiple assets. Thus, systematic risk can be caused by interest rate changes, inflation or deflation, economic recessions, political instability, and global crises (like COVID-19 or oil shocks). Systematic risk has an impact on investors because it cannot be eliminated through diversification; it affects all assets, regardless of industry or company; influences the overall return of a portfolio; investors are compensated for bearing this risk; and high beta stocks are more sensitive to systematic risk.

Unsystematic risk can be caused by company mismanagement, product recalls, labor strikes, legal issues, and industry-specific regulations. The impact of unsystematic risk can be reduced or eliminated through diversification; it affects only individual companies or sectors; well-diversified portfolios will see little impact from any single unsystematic event; and it is not compensated for in expected return models.

Diversification is a technique for reducing risk by combining assets that behave differently in response to the same stimuli. Unsystematic, or specific risk, is the risk associated with one individual security. Factors that impact one security include things such as management changes, operation disruptions, or recalls. If you hold enough securities, the impact of one of these events that affects a single company is minimal on your overall portfolio. This risk, therefore, can be diversified away. Unsystematic risk does not factor into an investment's risk premium since this type of risk can be diversified away.

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5d. Recommend investments that take advantage of diversification

How can an investor lower their risk through diversification?
What is the impact of correlation on portfolio diversification?
How many different assets are needed to create a diversified portfolio?

Diversification follows the old advice to "not put all your eggs in one basket". A diversified portfolio allows an investor to maximize return while minimizing risk. By holding multiple assets, an investor reduces the overall risk of losing because of negative results with one asset. If you hold only one stock and that company has financial trouble, you will lose much of your investment. If you hold ten stocks and one of them has financial trouble, the overall impact on your return will be less.

To obtain the optimal gains from diversification, investors should combine assets with limited correlation (a statistical measure that indicates the degree to which two or more assets move in relation to each other, ranging from -1 to +1, where values closer to 0 indicate little relationship between asset movements). A positively correlated asset will respond in the same direction to an event. Negatively correlated assets will move in opposite directions of an event.

An example of positively correlated stocks might be car and tire manufacturers. Both will gain if car demand increases. Negatively correlated stocks could be sunscreen and umbrella manufacturers.

Research has shown that a portfolio with 30 stocks will enjoy most of the gains from diversification. However, these 30 stocks must not be in the same industry or region to benefit from diversification.

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5e. Discuss CAPM measures and their components.

What is the CAPM used for?
What are the assumptions underlying the CAPM?
What does Beta measure?

The capital asset pricing model (CAPM) is a financial model used to price securities by accounting for the relationship between risk and return. CAPM determines the asset's rate of return, assuming it will be added to a well-diversified portfolio by accounting for the asset's systematic risk. The CAPM relies on beta to express the asset's risk.

The CAPM is based on several key assumptions that simplify the real world to make the model analytically tractable. These assumptions are crucial to understanding both the strengths and limitations of CAPM. Some of the key assumptions include: investors are rational and risk-averse, markets are efficient, all investors have homogeneous expectations, investors can borrow and lend freely at the risk-free rate, a single-period investment horizon, no taxes or transaction costs, all assets are perfectly divisible and liquid, returns are normally distributed, and only systematic risk matters.

Beta measures how a specific asset fluctuates compared to the overall market. Beta is determined by looking at the individual stock's past returns compared to the overall market's past returns, and seeing how correlated the returns are. A beta of less than one means the stock is less risky than the overall market, a beta equal to one is the same as the market, and a beta greater than one means the stock is riskier than the overall market.

CAPM shows that investors are only rewarded for bearing systematic risk since unsystematic risk can be mitigated by constructing a diversified portfolio.

Using the CAPM model, the stock's expected return equals the risk-free rate of return plus beta times the difference between the expected return on the market and the risk-free rate. The risk-free rate is the rate that short-term T-bills pay.

Since there is virtually no chance of losing money on an investment in government-issued short-term T-bills, they are used as a proxy for the risk-free rate. This is the "rent" investors demand for giving up the use of their funds, even though they know they will get it back. The market's expected return is usually approximated by the return for the S&P 500 or a similar index. Beta can be calculated or looked up through many investment sites. The rate calculated by using CAPM can thus help determine the appropriate stock price investors should be willing to pay – the price that will project the return determined by the model.

\(E(R_i)=R_f+\beta (E(R_m)-R_f)\)

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Unit 5 Vocabulary

This vocabulary list includes terms you will need to know to successfully complete the final exam.

beta
capital asset pricing model (CAPM)
correlation
diversification
expected value
portfolio
probability
return
risk
systematic risk
unsystematic risk