Chapter 13 - FIN320
How do you calculate portfolio beta?
- is ascertained just like the expected returns of that portfolio. The weight of assets in a portfolio is multiplies with their respective beta to ascertain the portfolio beta. Example: Bp=W x B + W x B
Is it possible that risky asset could have a beta of zero? 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?
-Beta is the measure of the riskiness of an asset. If beta is zero for an asset, then the expected return is equal to the risk free asset. Therefore, risky asset will NOT have a beta of zero. -Expected return of an asset with beta zero is equal to risk free asset. -YES it is possible that a risky asset could have a negative beta as it carries the negative risk premium due to the portfolio can be diversified.
What is the capital asset pricing model (CAPM)? What does it tell us about the required return on a risky investment?
-Capital asset pricing model (CAPM) is the equation of the SML (Security market line) showing the relationship between expected return and beat. -CAPM tells us the amount of systematic risk present in a particular asset or portfolio, relative to that in an average asset.
True or False : The expected return on a risky asset depends on that asset's total risk. Explain?
-FLASE, the results should be added in order to calculate the beta of the portfolio
Classify the following events as mostly systematic or unsystematic. Is the distinction clear? 3.Oil prices unexpectedly decline?
-The decline in oil prices effect the oil prices all over the country. This risk cannot be avoided. Hence, it is mostly a systematic risk
Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp's stock to change price: 3. The government reports that economic growth last year was 3 %, which generally agreed with most economic forecasts.
-The economic growth rate is a macroeconomic factor and changes in it against the forecast of economists cause to increase or decrease the systematic risk. - Therefore, the stock price will NOT change.
Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp's stock to change price: 1. The government announces that inflation unexpectedly jumped by 2 % last month.
-The increase in inflation rate will cause an increase in systematic risk. Thus, the market prices in general will fail. Also, the stock price of BWC will fall.
If a portfolio has a positive investment in every asset, can the expected return on the portfolio be greater than on every asset in the portfolio? Can it be less than that on every asset in the portfolio?
-The portfolio has positive investment, the expected return of the portfolio is neither greater than the returns of every asset, nor lesser than the returns of every asset.
What is the primary determinant of the cost of capital for an investment?
-The primary determinant of the cost of capital for an investment depends primarily on how and where the capital is raised. The cost of capital depends on the use of funds and not the source of funds. The source of funds which has less cost of capital involves high risk. Hence the cost of source of funds is compared with the risk involved.
You own a portfolio equally invested in a risk free asset and two stocks. If one of the stocks has a beta of 1.32 and the total portfolio is equally as risky as the market, what must the beta be for the other stock in your portfolio?
1 = 0 + 0.44 + Beta of other stocks x 1/3 Beta of other stock x 1/3 = 1 = 0.44 Beta of other stock = 0.56 x 3 Beta of other stock = 1.68 (Answer)
Unexpected return : New announcements?
1. Fall in interest rate 2. Sales made by the company 3. Government released GDP 4. Innovation made by the company.
Two types of risk?
1. Systematic risk 2. Unsystematic risk
What are the two basic parts of a return?
1. is expected return 2. unexpected return
Stock Y has a beta of 1.2 and an expected return of 11.4%. Stock Z has a beta of .80 and an expected return of 8.06%. if the risk-free rate is 2.5% and the market risk premium is 7.2%, are these stocks correctly priced?
Apply the principle of reward to risk ratio and verify the correctness of price of Stock Y and Stock Z -Reward of Stock Y/Risk of Stock Y = Reward of Stock Z/Risk of Stock Z -E(Rstock y) - Rrisk free asset / Bstock Y = E(Rstockz) - Rrisk free asset/Bstock z 0.114-0.025/1.2 = 0.0806 - 0.025/ 0.80 0.0742 = 0.0695 Conclusion : The principle of reward to risk does NOT hold good for the stock Y and Z because reward is hight than its risk for stock Y. Therefore the stock prices are not correctly priced.
A stock has a beta of 1.5, the expected return on the market is 10.3 % and the risk free rate is 3.8 %. what must the expected return on this stock be? (using the CAPM)
E(Rstock) = R risk-free + ((E(Rmarket)-R risk free)) x Bstock = 0.038 + (0.103 - 0.038) x 1.5 = 0.038 + 0.07475 Expected return on stock is = 0.1128 or 11.28%
True or false : The most important characteristic in determining the expected return of well-diversified portfolio is the variance of the individual asset in the portfolio. Explain?
FALSE - The most important characteristic in expected return of a well diversifiable is the variance of the asset compared to the portfolio.
What is the fundamental relationship between risk and return in well-functioning markets?
In an active, competitive markets , must have a situation. This is the fundamental relation between risk and return.
Equation for (total portfolio value)?
Number of shares of stock A times stock price of stock A plus Number of shares of stock B times stock price of stock B
Equation for portfolio weight?
Number of stock A multiplied by Stock price of stock A divided by Total portfolio value
You have $10,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 11.5% and stock Y with an expected return of 9.4%. If your goal is to create a portfolio with an expected return of 10.8%, how much money will you invest in Stock X? Stock Y?
Step 1 : Compute the portfolio weight of stock X. W=0.690476 -Since the sum of weights of various assets in portfolio 1, assumer portfolio weight of stock Y as (1-Wx) Step 2 : Compute the amount invested in stock X = 6,904.76 Step 3 : Compute the amount invested in stock Y =3,095.24
You own a portfolio that has $2,650 invested in Stock A and $4,450 invested in Stock B. If the expected returns on these stocks are 8% and 11%, what is the expected return on the portfolio?
Step 1 : Total portfolio vale = (2,650+4,450)=7,100. Step 2 : Stock A 2650 / 7100 = 0.3732 X 0.08 = Expected portfolio return 0.02986 (Stock A) Step 3: Stock B 4450/7100 =0.6268 X 0.11 = 0.06895 Expected return portfolio (Stock B) Step 4 :(Stock A EPR + Stock B ERP) = 0.0988 or 9.88%
Define Portfolio?
The group of total assets invested in stocks and bonds collectively held by the investor is referred to as portfolio.
Define systematic risk?
The overall market risk which affects the large number of assets in the market. This risk cannot be diversified, and it has a very wide effect on the market and that is why it is called market risk as well.
Why is some risk diversifiable? What are some risks nondiversifiable? Does it follow that an investor can control the level of unsystematic risk in a profolio, but not the level of systematic risk?
There are some risks that are created because the profolio composition. Some risks are not diversifiable because they are the basic risk of the overall system. Systematic risks cannot be reduced but unsystematic risks can be reduced through a better diversification of stocks. So the investor can control unsystematic risks but not systematic risks.
Unexpected return def?
Unexpected return is the return which is cannot be expected by the shareholders due to new information or new announcements. The unexpected return is depending on the new informations or new announcements
In words, how do we calculate the variance of the expected returns?
We first determine the square deviated from the expected return. Then we multiply each possible square deviated by its probablity.
Define unsystematic risk?
has a effect on a single asset or a small number of assets in the market, and this risk is associated with a single company or asset and that is why it is also called unique or asset- specified risk
Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp's stock to change price: 4. The directors of Big Widget die in a plane crash.
- An important member from management passed away which will decrease the managerial capacity of the managing team. This loss of will INCREASE the unsystematic risk. -Therefore the stock price of BWC will decrease.
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 abut the portfolio beta?
- If a portfolio has a positive investment in every asset, the portfolios standard deviation can be less than that on every asset in the portfolio because if the returns of each individual asset in the portfolio are very close to each other, them the portfolios standard deviation will be very low. - On the other hand, the portfolio beta will never be less than that on every asset in the portfolio because it is calculated as the weighted average. So the portfolio beta will always be less than the greatest assets beta an created than the lowest asset beta.
What is the systematic risk principle?
- Is a form of market risk which effects the overall market an portfolio or investments or decisions risk and return. -is the expected return on a risky assets systematic risk.
What is meant by the term cost of capital?
- Is the expected return that is required on new investments. The expected return on investment is what a company must earn on its capital investment in order to break even. -it is alternatively referred to as the opportunity cost of capital r the required rate of return. The cost of capital is generally calculated on a weighted average basis.
What is the security market line? Why must all assets plot directly on it in a well-functioning markets?
- Security market line (SML) is a positively slopped line displaying the relationship between expected return and beta. -In a well functioning market, a market portfolio is made up of all these assets. Hence, all the assets in the market must plot on same SML.
Why are some risks diversifiable? Why is some risk not diversifiable?
- Some risk diversifiable as the risk of asset is associate with generic causes which can be eradicated through diversification. Some risk not diversifiable as the systematic risk cannot be eradicated because the markets take exposure of those risks
Why cant systematic risk be diversified away?
- Systematic risk cannot be diversified away as it includes interest rate risk, recession and wars which affect the overall market and cannot be eradicated.
Suppose the government announces that, based on a just completed survey, the growth rate in the economy is likely to be 2 percent in the coming year, as compared to 5 percent for the past year. Will security prices increase, decrease or stay the same following this announcement? does it make any difference whether the 2 percent figure was anticipated by the market? Explain.
- The price securities reflect the supply and demand of the market an as well as the health of the market. - In this case, the growth rate of the market of past year is 5% and for the next year the government is focused the growth rate to be 2%. On ideal basis, all security prices will reduce by 2%. This is because the growth rate is 2% from 5%. -After this announcement of reduced growth rate the price would decrease. -Theoretically, it does not make any difference if the same lower growth was predicted by the market.
What is the principle of diversification?
- The principle of diversification suggests that invest the total investment in different financial assets or investment to lower the risk.
Classify the following events as mostly systematic or unsystematic. Is the distinction clear? 1.Short-term interest rates increase unexpectedly.
- The short term interest rate effect the market as a whole. Therefore, unexpected increase in short term interest rates is mostly systematic.
What happens to the standard deviation of return for a portfolio if we increase the number of securities in the portfolio?
- The standard deviation falls in the number of securities increase as the standard deviation of portfolio return an the number of securities in the portfolio have indirect relation.
Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp's stock to change price: 5. Congress approves changes to the tax code that will increase the top marginal corporate tax rate. The legislation has been debated for the previous six months.
- There will NOT be any changes in the systematic risk at this change in tax code was expected. - The price of stock in general an or specifically will not get affected due to approval of congress on tax code.
Classify the following events as mostly systematic or unsystematic. Is the distinction clear? 6.A supreme court decision substantially broadens producers liability for injuries
-An apex court decision effects all producers. All enterprises in that industry is affected by this decision. Thus, its systematic risk.
Classify the following events as mostly systematic or unsystematic. Is the distinction clear? 4.An oil tanker ruptures, creating a large oil spill
-An oil tanker ruptures spill oil, this is abnormal loss for enterprise. This risk effects the enterprise only an not the market. Thus is mostly unsystematic risk.
A stock has an expected return of 10.2 %. the risk free rate is 4.1 %, and the market risk premium is 7.2%. What must the data of this stock be? (using CAPM)
-E(Rstock) = R risk-free + ((E(Rmarket)-R risk free)) x Bstock 0.102 = 0.041 + 0.072 x Bstock 0.061 = 0.072 x Bstock Bstock = 0.061/0.072 Bstock = 0.85 %
If an investment has a positive NPV, would it plot above or below the SML? Why?
-If an investment has a positive NPV, it would plot above the SML because expected returns are superior to what the financial markets offer for the same risk. -To determine whether an investment has a positive NPV we compare the expected return on that new investment to what the financial market offers on an investment with the same beta.
Under what conditions will a company's announcement have no effect on common stock prices?
-If shareholders able to predict the new information or new announcements than there will be no change in the common stock price. -If shareholders predict that interest rate is fall by 2% and the actual fall of interest rate is exactly 2%. Than there will be no affect on the stock price because predicted fall of interest rate is equal to actual fall of interest rate. -Therefore, announcements will have NO affect on the stock prices if predicted information is equal to actual information
Classify the following events as mostly systematic or unsystematic. Is the distinction clear? 2.The interest rate a company pays on its short term debt borrowing is increasing by its bank?
-If the short term borrowing interest rate is increased by Bank, it is related to the company. it does NOT affect the whole market but only the company. Therefore, it is mostly unsystematic risk.
Classify the following events as mostly systematic or unsystematic. Is the distinction clear? 5.A manufacturer loses a multimillion dollar product liability suit
-Loss on liability suits effects the performance of the manufacturing company specifically. This lose may be mitigated by entering new contracts or other measures. Thus, it mostly unsystematic risk.
You own a stock portfolio invested 20% in stock Q, 30% in stock R, 35% in stock S, 15% in stock T. The betas for these four stocks are .84, 1.17, 1.08, and 1.36. What is the portfolio beta?
-Stock Q ( .20 X 0.84 ) = 0.168 -Stock R ( .30 X 1.17 ) = 0.351 -Stock S (0.35 X 1.08 ) = 0.378 -Stock T ( 0.15 X 1.36 ) = 0.204 Portfolio Beta = 0.168 + 0.351 + 0.378 + 0.204 = 1.101
Differences between two types of risks?
1. Systematic risk has an impact on the large number of assets an has large impact on the market, however unsystematic risk is associated with a single asset or a company or a small number of assets. 2. The systematic risk cannot be diversified, however unsystematic risk can be diversified.
What does a beta coefficient measure?
Beta coefficient measures the amount of systematic risk that is risky asset has in comparison to that in average risky asset. Beta also is known as sensitivity analysis. Beta also measures the volatility or systematic risk of security or portfolio.
A stock has an expected return of 12.15%, its beta is 1.31, and the expected return on the market is 10.2%. What is the risk-free rate be?
E(Rstock) = R risk-free + ((E(Rmarket)-R risk free)) x Bstock =0.01212/0.31 Rrisk-free = 0.0391 or 3.91 % Rate of return on risk free asset is 3.91%
A stock has expected return of 11.05 %, its beta is 1.13 % and the risk free rate is 3.6%, what must the expected return on the market be?
E(Rstock) = R risk-free + ((E(Rmarket)-R risk free)) x Bstock E(Rmarket) = 0.065929 + 0.036 = 0.101929 or 10.19 % Return on market is 10.19%
Expected return def?
Expected return is the return predicted by the shareholders of the company. This was predicted by shareholders, from the information they acquired from the market.
What does E(R) stand for in the expected return on a portfolio return?
Expected return of asset
What does the E(R) stand for in the expected return on a portfolio formula?
Expected return of portfolio
How do we calculate the expected return on a portfolio?
Expected return on a portfolio is calculated as the summation of weight for each asset multiplied by expected return on asset.
How do you calculate the expected return on a security?
Expected return on a security is equal to the sum of the possible returns multiplied by their probabilities.
Based on the following calculate the expected ream: State of economy ( Recession & Boom) Probability of State of Economy (.20 & .80) Portfolio return if state occurs (-.14 & .17)
Recession : (0.20 x -0.14) = -.0280 Boom : (0.80 x 0.17) = 0.136 - Add (.0280 + 0.136) Expected return, E(R) = 0.108 or 10.80%
Calculate the expected return : State of economy ( Recession & Normal & Boom) Probability of state of economy (.10 & .60 & .30) Portfolio Return if state occurs (-.18 & .11 & .26)
Recession: 0.10 X -.18 = -0.018 Normal: 0.60 X 0.11 = 0.066 Bom: 0.30 X 0.26 =0.078 Expected Return E(R) = -.018 + 0.066 + 0.078 = 0.126 or 12.60%
What are portfolio weights for a portfolio that has 135 shares of stock A that sells for $48 per share and 165 shares of stock B that sells for $29 per share? (What are the steps)
Step 1: Compute the total portfolio value. Step 2:Compute the portfolio weight of stock A in the total portfolio value. Step 3: Compute the portfolio weight of stock B in the total portfolio value.
Define portfolio weights?
The percentage of particular asset value in the total portfolio value is referred to as portfolio weight. also is a group of stocks and bonds or assets that an investor holds or invest into for earning profits.
Indicate whether the following events might cause stocks in general to change price, and whether they might cause Big Widget Corp's stock to change price: 2. Big Widget's quarterly earnings report, just issued, generally fell in line with analysts expectations.
The quarterly earnings of BWC will increase or decrease the risk associated with the company only that is unsystematic risk. -Therefore, the price of stock will NOT change.
Is there a simple relationship between the standard deviation on a portfolio and the standard deviation of the assets in the portfolio?
The relationship between the standard deviation of portfolio and standard deviation of the asset is the portfolio is not simple. Because it also considers the correlation.
What does (x) stand for in the expected return on a portfolio return?
Weight of asset
