Chapter 8 -Finance
CAPM Assumptions
(SML) •Investors hold well-diversified portfolios •Competitive markets •Investors are risk averse •Borrow and lend at the risk-free rate •No brokerage charges •No taxes •Investors have homogeneous expectations
Portfolio
A collection of financial assets and securities
Systematic Risk
A stock's contribution to the market risk of a well-diversified portfolio. According to the Capital Asset Pricing Model (CAPM), this risk can be measured by a metric called the beta coefficient, which calculates the degree to which a stock moves with the movements in the market. A well-diversified portfolio will exhibit a minimum of unsystematic, or company-specific risk. The portfolio's remaining risk represents market risk, which cannot be diversified away with addition of more assets. Each stock's contribution to market risk is termed systematic risk.
maturity risk premium
As interest rates rise, bond prices fall, and as interest rates fall, bond prices rise. Because interest rate changes are uncertain, this premium is added as a compensation for this uncertainty. reflects the risk associated with interest rate changes. Interest rate risk refers to the capital loss that an investor would suffer when the value of a bond decreases due to an increase in interest rates. The longer the maturity of a bond, the higher is the risk, thus causing a higher maturity risk premium for long-term bonds.
Which kind of stock is most affected by changes in risk aversion? (In other words, which stocks see the biggest change in their required returns?)
High beta stocks
Nominal Risk Free Rate
It is calculated by adding the inflation premium to real rate of return. is the rate on a riskless security that includes an inflation premium for expected inflation
subjectively-determined probabilities
Probabilities determined based on opinions and personal expectations
Liquidity Premium
Some liquid assets can be converted into cash quickly at fair market value, and other assets have different levels of liquidity. Because an investor carries the risk of not being able to sell a security and convert it into cash quickly enough to prevent or minimize loss, a liquidity premium is added to the equilibrium interest rate.
calculate the beta coefficient of Stock j:
Stock J's standard deviation/markets S.D. X Correlation between Stock j and the market
The required rate of return can be broken down further into several components such as
The inflation premium, default risk premium, liquidity risk premium, and so on.
Market Segmentation Theory
The theory that the shape of the term structure of interest rates implies that the rate of interest for a particular maturity is determined solely by demand and supply for a given maturity. This rate is independent of the demand and supply for securities having different maturities. balance of supply of demand. Some prefer short, medium, or high return
default risk premium
This is the premium added as a compensation for the risk that an investor will not get paid in full. refers to the risk that a borrower will default, which means that the borrower will not make payments as committed. Based on the credit quality and chances of default, ratings are assigned to bonds. The higher the bond rating, the lower its default risk and added default risk premium, thus resulting in a lower interest rate. If a corporate bond has the same maturity and the same marketability as a U.S. Treasury bond, its default risk premium will be the difference in the interest rate offered by the corporate bond and the interest rate on the U.S. Treasury bond.
Inflation Premium
This is the premium added to the real risk-free rate to compensate for a decrease in purchasing power over time. is added to the real risk-free rate to compensate for the expected increase in the value of goods and services due to inflation. The inflation premium is calculated based on the expected changes in inflation over the entire life of the security, not the rate of inflation in the past—but you can use past inflation rates to calculate the expected rate of inflation. Countries like Germany, Japan, and Switzerland have had lower inflation rates in the past than the United States and thus lower premiums and, consequently, lower interest rates. Italy and several South American countries have had higher inflation rates than the United States and thus higher premiums and interest rates.
Real rate of return
This is the rate on short-term U.S. Treasury securities, assuming there is no inflation. is the rate that would exist in an inflation-free world on a riskless security. United States Treasury securities are considered to be riskless securities, since they are backed by the U.S. government. Considering there is no inflation, the rate on riskless U.S. Treasury securities would be considered the real risk-free rate. This rate is not static but keeps changing based on the expected rate of return on productive assets traded among investors and borrowers. The real rate of return also depends on an investor's time preference for current versus future consumption.
Securities can be arranged in the following order, from lowest risk to the highest risk:
U.S. Treasury bills; long-term U.S. government bonds; high-quality corporate bonds; high-quality preferred stock; low-quality corporate bonds, also called junk bonds; high-quality common stock; and speculative common stock.
Risk-free rate can be split into
a real risk-free rate and an inflation premium
Required rate of return can be split into
a risk-free rate and a premium for risk
Diversifiable, or unsystematic, risk can be reduced by
adding more securities to the portfolio. However, because systematic risk is associated with the entire market, risk can be reduced by investing in different markets through a process called hedging.
The unsystematic risk component of the total portfolio risk can be reduced by
adding negatively correlated stocks to the portfolio.
A portfolio's risk is likely to be smaller than the
average of all stocks' standard deviations, because diversification lowers the portfolio's risk.
Diversification refers to the
combination of unrelated activities investing in unrelated businesses buy stocks that don't do the same things ex. when cold buy more parkas, not ice cream. Cancel each other out
Securities issuance
contains default risk, seniority risk, and Marketability Risk
Investors will see that they expect to
earn more than they should based on the risk level
Investors will stop buying when the
expected return equals the required return
Fairly valued when
expected return is equal to its required return
a high-beta stock will experience a
far greater change in required return than a low-beta stock.
The steeper the slope of the SML, the
higher the level of risk aversion. and higher the risk premium added to the required rate of return.
The benefits of diversification are greater when stocks are not
highly correlated. Returns on stocks from the same sector are likely to have greater correlation than if you choose stocks from the different sectors. For that reason, you would expect a large portfolio of randomly selected stocks across many sectors and markets to have a lower standard deviation.
Investors can further reduce risk by
holding both U.S. stocks and stocks from the international markets in their portfolios. Because U.S. and international stocks are not perfectly correlated, adding international stocks to a portfolio helps diversify and reduce risk.
Expected Value
is a statistical measure of the most likely outcome •Probability weighted average
beta coefficient
is a statistical measure of the stock's relation with the market—that is, the extent to which the return on a stock rises and falls with the changes in the market's return. Analysts generally use historical data to calculate the beta and use it as an estimate of the stock's volatility relative to the market.
the tighter the probability distribution
lower risk and taller one
Portfolio risk consists of
market risk, also called systematic risk, and diversifiable risk, also called unique risk or unsystematic risk.
risk premium
maturity risk. All of these theories have different times of maturities and all issued by govt.
more spread out distribution
more risky and less tighter prob.
If there were no uncertainty
no risk, an investment's actual returns would be the same as its expected returns.
An average stock is said to have a beta of 1.0, which means that
on average it moves in the same direction and with the same magnitude as movements in the market. This means that the average stock is positively correlated with the market.
An investor can become diversified by
owning more than one security
•Seniority Risk
part of Securities issuance •In event of default, which claims are paid first? paid first= less risk
Marketability Risk
part of Securities issuance •Is it easy to find a buyer when you wish to sell?
•Default Risk
part of Securities issuance •Possibility that interest and principal will not be repaid as promised •
every security should
plot on SML invest in something that gives you systematic risk. 2 plots A and B not plotting on line so those securities are mispriced if price goes down then HPR goes up
The security market line (SML)
plots the results derived from the Capital Asset Pricing Model (CAPM), which is based on the proposition that a stock's required rate of return is equal to the risk-free rate plus a risk premium that represents the compensation that an investor needs for the additional risk. graphs the relationship between an asset's beta and its required return.
Because the stocks within the portfolio are not perfectly correlated (ρ < 1), the portfolio benefits from diversification. Hence, the
portfolio's standard deviation must be less than the weighted average of the risk of the individual securities. The weighted average of risk of the individual securities is 34%, so the portfolio's standard deviation must be less than 34%.
Inflation premium is built in to
preserve purchasing power
A single stock has a great deal of company-specific risk. If you add stocks, which are less than perfectly positively correlated, to the portfolio, you will
reduce the risk (as measured by the standard deviation) of the portfolio.
Portfolio Risk
refers to the possibility that an investment portfolio will not generate the investor's expected rate of return.
Market risk
refers to the systematic risks in the equity markets that are affected by macroeconomic conditions and external factors.
Coefficient of variation is a
relative measure of risk is a measure of variability that scales the standard deviation by the expected return of an asset. measures both risk and return, is the ratio of the standard deviation to the expected rate of return and depicts the trade-off between risk and return
Diversifable Risk
represents the risk that is inherent to the stocks in the portfolio. It is risk associated with unexpected events that affect the returns associated with a particular stock. Some examples include lawsuits, strikes, or product failures.
Undervalued when
required returns (r̂f) are less than their expected returns. These conclusions are verified by the graph. Stock C lies on the SML, whereas Stocks A and B lie above it.
Corporate bonds are not
risk free
Graphical Interpretation
risk free rate= vertical line/y intercept MRP= slope on vertical line Beta= x RRR=y
Diversification can reduce
risk if some securities go up when others go down
An investment is
risk-free only if the cash flows (returns) are known with certainty ex;•US Treasury bills (i.e., short-term) backed up by US govt.
Standard deviation measures
standalone risk
beta measures a
stock's contribution to the risk of a well-diversified portfolio. Beta measures the risk of a given security relative to the overall market, which is considered to be a large, diversified portfolio.
Total risk can be divided into
systematic and unsystematic risk
Riskiness is measured in
terms of the variability of the returns
The risk-return relationship merely states
that investments in high-risk securities increase the possibility of high returns.
If investors become less risk averse,
the SML will become flatter
Financial risk is the
the extra variability due to the choice in financing, i.e., leverage
Expectations Theory
the proposition that the interest rate on a long-term bond will equal the average of the short-term interest rates that people expect to occur over the life of the long-term bond
As the level of risk in an investment increases,
the required rate of return increases
if a stock has a beta that is greater than 1.0, it means that
the stock's positive and negative returns will be greater than the market's returns. Investors should expect a higher rate of return from stocks with higher betas.
Liquidity Preference Theory
the theory that investors demand a risk premium on long-term bonds higher return if you give up money for long time
Maturity risk
theories explain shape of yield curve •Impact of interest rate changes during the life of the investment Yield curve •Expectations theory •Liquidity Premium theory •Market Segmentation theory
When investors become risk-averse
they require more compensation for their risk, which leads to a steeper SML and a higher risk premium.
a security with a beta of zero is completely
unaffected by this change in investor risk aversion.
Risk represents the
variability of returns, and can be defined as the possibility that actual future cash flows (earnings or returns) will not be the same as the forecasted or expected cash flows. Risk represents uncertainty, which causes actual results to differ from the expected results.
Systematic risk is that
which affects the entire economy systematic cannot be diversified
Example of risky outcome
winning lottery
expectations theory of interest rates
you can infer expected future short-term rates by comparing spot short- and long-term rates. If future short-term interest rates are expected to rise, the yield curve will tend to be upward sloping. In contrast, a downward-sloping yield curve reflects an expectation of declining future short-term interest rates.
Normal distribution is the
•'Bell-shaped curve' •Normal distribution can be described entirely by its mean and standard deviation •Z score •Approximately two-thirds (68.26%) of outcomes are within one standard deviation of the mean. 95.44% of outcomes are within 2 standard deviations and 99.74% are within 3 standard deviations You can find probabilities of any z by using Table V
It plots above the SML
•- it is underpriced
Finding required return using b
•A security with the same risk characteristics as the market should have the same expected return •If bj = 1, then kj = rm •We can use the same formula for other bs
standard deviation
•Absolute measure of risk •Square deviations so positive and negative deviations don't cancel each other out •Weight by probabilities •Take square root so it is measured in same units is the weighted average of the deviations from the expected value. It indicates the extent to which the actual value is above or below the expected value
three special cases of correlations
•Case I: Perfect Positive Correlation (r=1) •No risk reduction is possible without decreasing the expected return • •Case II: Zero Correlation (r =0) •When r <1, diversification can reduce the risk of the portfolio below the weighted average of the individual securities' risk • •Case III: Perfect Negative Correlation (r =-1) •With perfect negative correlation, it is possible to completely eliminate risk by buying the securities in the right proportions
Risk of a Portfolio
•Combining securities with less than perfect positive correlation can reduce the risk of the portfolio
Practical problems with CAPM
•Estimating expected future market returns •Determining an appropriate rf •Determining the best estimate of b •Investors don't totally ignore unsystematic risk •Betas are frequently unstable over time •Required returns are affected by macroeconomic factors •Other factors besides overall market return may influence required return (growth vs. value, firm size) b can change over time
Correlation, p
•If one generally goes up when the other does, they are positively correlated (r>0) •If one generally goes down when the other goes up, they are negatively correlated (r<0) •If one always moves in proportion to the other, they are perfectly correlated (r =1 or r =-1) •If there is no pattern between the two payoffs, they are uncorrelated (r =0)
Efficient Frontier
•If we have more than two risky securities, we get a set of possible portfolios •The efficient frontier is the set of efficient portfolios pick securities along the top line between point A and B never pick investment within interior •When we also consider the risk-free asset, all investors should prefer the same portfolio of risky assets •Red line is Capital Market Line •m is the market portfolio
Diversification and Risk
•In well-diversified portfolios, the unsystematic risk can be nearly eliminated •The only risk that needs to be compensated is systematic risk greater systematic risk= greater risk
Beta of a Portfolio
•Like the expected value, the beta of a portfolio is a weighted average of the individual securities' betas standard deviation is not a weighted average
Fisher won the
•Nobel Prize in Economics for describing the relationship between real interest rates, nominal interest rates, and inflation where R is the nominal rate, r is the real rate, and h is inflation
Security Market Line
•Required return on security j is equal to the risk-free rate plus a risk premium
Expected Value of a Portfolio
•The expected value (payoff) does not depend on the level of risk •The expected value of a portfolio is a weighted average of the securities' expected returns where the weights are the portfolio weights
•Consider a situation where you have $100 today and a loaf of bread costs $1.00. You can buy 100 loaves now. Suppose you could invest that $100 at a 5% interest rate for a year •The price of a loaf of bread will increase 2%. •The extra 2.94% compared to the original number of loaves represent the increase in your purchasing power.
•This is the nominal interest rate. •This is the inflation rate. •At the end of the year, you will have $105 and you can buy 102.94 loaves of bread (=$105/$1.02) •This is the real rate of interest.
Beta, b
•We measure security j's systematic risk with b •By definition, the beta of the market portfolio is 1. • •We often find b by plotting rj vs rm and finding the slope. This is called the characteristic line. can have covariance outside of -1 and 1 plot security returns and if b<1 than less exposure to systematic risk
Sometimes, standard deviation is too
•absolute a measure of risk •Consider two projects - both have payoffs with a standard deviation of $1,000. Project A has an expected payoff of $10,000 while Project B has an expected payoff of $10,000,000. •Which seems more risky to you? project A
An efficient portfolio has the
•highest expected return for a given level of risk • •An efficient portfolio has the lowest level of risk for a given level of expected return whichever they choose depends on the level of risk conversion
Business risk is that which
•is inherent in the operations of the company - business cycle, technology, market power •operations side if company does worse=interest rate becomes bigger amount
Risk
•is the possibility that actual cash flows (or returns) will be different than expected cash flows (or returns) greater risk=greater return
If a security plots off of the SML
•it is mispriced! •As investors identify it as mispriced, they will want to either buy or sell (depending on whether it is underpriced or overpriced), which will cause the price to move back to where it should be
A portfolio is made of
•multiple securities, like stocks and bonds •We can assign weights to each security to represent how much of the portfolio is invested in each security •The sum of the weights must be 1 (or 100%) •Let wi be the weight of security i If we just have two securities, use wA and wB portfolio weights can be (-) just means you are borrowing
A diversified company would
•operate more than one type of business •ex; General Electric reports segments operating in "Power, Renewable Energy, Oil & Gas, Aviation, Healthcare, Transportation, and Energy Connections & Lighting". It used to have segments with TV Broadcasting and Financial Services.
In equilibrium, all securities should
•plot on the SML •All securities should provide the same reward per unit of risk
Unsystematic risk is the
•portion of the variability which is caused by factors unique to the security •Unsystematic risk can be diversified away
As they buy,
•the balance of supply and demand will push the price up •As the price goes up, the expected return will go down
Risky investments have
•uncertain payoffs (i.e., are variable)
