Investments Exam 1
Which of the following is not an assumption of the simple CAPM? I. Individual trades of investors do not affect a stock's price. II. All investors have the same level of risk aversion. III. All investors have access to the same information and analyze securities in the same way. IV. All investors plan for an identical holding period. A) Statement I B) Statement II C) Statement III D) Statement IV
B Explanation: In a theoretical CAPM world investors only differ in terms of their levels of initial wealth and their degrees of risk aversion.
An investor puts up $5,000 but borrows an equal amount of money from his broker to double the amount invested to $10,000. The broker charges 7% on the loan. The stock was originally purchased at $25 per share, and in 1 year the investor sells the stock for $28. The investor's rate of return was ________. A) 19% B) 17% C) 12% D) 14%
B Explanation: Number of shares = $10000/$25 = 400 Profit = ($28-$25)*400 - $5,000(0.07) = 850 Investment = $5,000 Return = 850 / 5,000 = 17% (stock increase-interest)/investment
Is the following scenario possible? Explain. 2 portfolios: A E(r)=20%, Standard dev.=35% B E(r)=30%, Standard dev.=25%
Possible. Under the CAPM, beta is the sole determinant of expected returns. It is possible that stock B, despite having a lower standard deviation, has a higher beta. CAPM doesn't say anything about standard deviation Only B and E(r) relationship matters
What is the difference between a primary and secondary market?
The primary market is the market where newly-issued securities are sold, while the secondary market is the market for trading existing securities. Corporations only receive money when they sell their new securities in the primary market, and then all subsequent trading occurs in the secondary market.
Components of effective costs of buying/selling stocks
bid-ask spread, brokerage fees, commissions, taxes..These reduce the amount received when selling stock and increase the cost incurred when buying stock.
correlation
-always some diversification benefit when correlation is less than 1 -lower correlation, the better
Margin Trading: Be able to compute...
oComputation of investment returns oComputation of margin % oComputation of price at which margin call occurs
Short Selling: Be able to compute...
oComputation of margin % oComputation of price at which margin call occurs
Capital Allocation: Be able to...
-Be able to construct CAL and know its properties -Capital Allocation Line is graphed with possible Expected Return, Standard Deviation pairs found by varying the choice of y. -Sharpe ratio=the slope of the cal -Vary your allocation (your y)
Initial Public Offerings
-IPO: First sale of stock by a formerly private company, sold on primary Mkt, registered with SEC and the sale is made to the investing public -Role of the investment bank/underwriter: issuing firm sells to the lead underwriter (Purchase securities from issuing company and resell them), and they sell to the investment bankers who then sell to private investors -Road show/book building: Issuer and banker put on "road show" for the purpose of book-building and pricing information (get to know how much investors are willing to pay) IPO's have an evidence of underpricing-Post-initial sale returns average 10% or more, IPO stocks tend to underperform for the first 3 years
Order Types
-Market Order: Executes immediately at best available price -Bid price: price at which dealer will buy security -Ask price: price at which dealer will sell security (The investor pays the ask when buying and receives the bid when selling. Dealer profits off the spread.) Price Contingent Orders-- -Limit Buy/Limit Sell: specifies price at which investor is willing to buy (sell)--entering the market -Stop Buy/Stop Sell: An order not to be executed until price point reached; used to protect against large losses--used when shorting or exiting the market -Reasons for using one over the other: Advantage--A market order will guarantee trade execution while price contingent orders may never occur Risks--May pay higher price depending on depth of market (i.e. # shares available at best quoted price), Other orders may be executed before yours resulting in a worse price, Prices may change prior to order execution Limit Order Book: list of unexecuted limit orders
Covariance and Correlation
-Measures the tendency of returns to move together or opposite each other (i.e. to co-vary) -Lower covariance/correlation → lower portfolio standard deviation. -Correlation Coefficient (𝜌): Like variance, covariance has units in percent squared; Correlation is simply a scaled version of covariance that's easier to interpret. (Ranges from -infinity to +infinity) -Portfolio expected return is a weighted average of the individual asset expected returns -But portfolio standard deviation is less than a weighted average and can even be lower than the standard deviation of either asset
Portfolio Systematic Risk
-Portfolio beta equals weighted average of individual security betas -Systematic risk cannot be eliminated through diversification -It represents a risk that is common to all securities systematic risk: market unsystematic: firm
Scenario Analysis
-Possible economic scenarios -Specify likelihood and return expected for each -Expected return: Mean value of distribution of possible returns -Variance: Expected value of squared deviation from mean, Units are percent squared -Standard deviation: Square root of variance, Units are in percent
Index Models
-Relates stock returns to returns on market index factors -Can be used to test models like the CAPM -Designed to help differentiate systematic vs. firm-specific risk Excess return (_𝑟𝑖−r𝑓): Rate of return in excess of the risk-free rate Beta (𝛽): Sensitivity of a security's returns to market movements -Beta of overall stock market = 1 -Cyclical stocks: Beta > 1 (high systematic risk) -Defensive stocks: Beta < 1 (low systematic risk) -the slope of the line. Stocks with higher betas tend to go up (down) more when the market is up (down) Alpha (𝛼): Stock's expected return beyond that explained by market factor(s). (Measures how much better or worse a stock does than the CAPM or other model predicts); Positive alpha is attractive to investors -the intercept of the line. Alpha shifts the whole line up or down. Firm-specific or residual risk (𝑒): Component of returns independent of the market factor (e.g. stock fluctuations due to unexpected events) -distance between each point and the best fit line (i.e. company may experience good or bad news in a specific month); reflected in error term, how far above line Security Characteristic Line (SCL): Best fit line for plot of the security's excess returns against excess returns of the market
Rates of Return
1) Arithmetic average: Sum of returns in each period divided by number of periods; doesn't account for compounding 2) Geometric average (time-weighted average): Compound period-by-period returns, find per-period rate that compounds to same final value; Single return that gives same cumulative performance as sequence of actual returns -Geometric averages always lower than arithmetic -assesses long-term performance 3) Dollar-weighted average return: Computed as internal rate of return (IRR) on investment, Periods when more money is invested are weighted more; accounts for timing of cash flows -equates the present value of cash in and outflows -penalizes fund managers for low returns
Three Rules For Portfolios
1)Rate of Return: Weighted average of returns on components, with investment proportions as weights 2)Expected Rate of Return: Weighted average of expected returns on components with portfolio proportions as weights 3)Variance of Rate of Return: Impacted by return correlation -Combining lower correlation assets yields increased diversification benefit Low returns on one asset are more likely to be offset by high returns on the other -Always some diversification benefit except when correlation = 1
The graph shows that the required return=15%. What is the alpha of a portfolio with a beta of 2 and actual return of 15%? A) 0% B) 13% C) 15% D) 17%
A A portfolio with a beta of 2 has a required return of 15% under the CAPM. We're told its actual return is 15% as well; therefore, its alpha is 0% (15 - 15%).
You short-sell 200 shares of Rock Creek Fly Fishing Co., now selling for $50 per share. If you want to limit your loss to $2,000, you should place a ____ order at a price of ___. A) stop-buy; $60.00 B) stop-buy; $40.00 C) limit-buy; $60.00 D) limit-buy; $40.00
A Explanation: A stop-buy order should be placed at $60, so the stock will be purchased to cover the short position if/when its price increases to this amount. The loss at this point would be $10 per share or $2,000 total. 2000/200=10 50+10=60
You sell short 200 shares of ABC Inc. that are currently selling at $50 per share. You post the 50% margin required on the short sale. If your broker requires a 30% maintenance margin, at what stock price will you get a margin call? (Ignore the potential effects of interest on borrowed funds and assume there are no dividends.) A) $57.69 B) $63.00 C) $71.42 D) $64.50
A Explanation: Account Value / (1+MMR) = $15,000 / (1 + .30) = $11,538.46 Margin Call Price = $11,538.46 / 200 shares = $57.69 *Account Value = Stock Sale of $10,000 (200*50) + $5,000 margin = $15,000 [account val/(1+mmr)]/#shares=marginal call price [15000/(1+.3)]/200
Which stock is likely to be less risky to an investor currently holding his or her portfolio in a well-diversified portfolio of common stock? Assume the SCL of stock A is given by RA -rf =-0.5%+0.1(Rm -rf),andtheSCLofstockBisRB -rf =-0.5%+0.8(Rm -rf). A) Stock A B) Stock B C) There is no difference between A or B. D) The answer cannot be determined from the information given.
A Explanation: For a well-diversified portfolio, beta is the appropriate measure of risk because firm- specific risk has been diversified away. Stock A has the smaller beta, since the slope of its best-fit line (SCL) is smaller; therefore, it is less risky to the investor. This can be seen from the graph or by looking at the market risk premium's coefficient in the equations.
You sold short 300 shares of common stock at $30 per share. If the initial margin is 50%, you must deposit ________. A) $4,500 B) $6,000 C) $9,000 D) $10,000
A Explanation: Stock position = 300($30) = $9,000 Investment = ($9,000)(0.50) = $4,500
Which of the following provides the best example of a systematic-risk event? A) The Federal Reserve increases interest rates by 0.50%. B) A strike by union workers hurts a firm's quarterly earnings. C) A senior executive at a firm embezzles $10 million and escapes to South America. D) Mad Cow disease in Montana hurts local ranchers and buyers of beef.
A Explanation: Systematic-risk events are events that impact the broader economy and are likely to have an impact on the value of most firms. A change in market interest rates has this effect, whereas the other three events are firm-specific or affect a relatively small number of firms.
Kaskin Inc. stock has a beta of 1.2 and Quinn Inc. stock has a beta of 0.6. Which of the following statements is most accurate? (Multiple Choice) a. The expected rate of return will be higher for the stock of Kaskin Inc. than that of Quinn Inc. b. The stock of Kaskin Inc. has more total risk than Quinn Inc. c. The stock of Quinn Inc. has more systematic risk than that of Kaskin Inc.
A higher Beta=higher E(r)
Suppose you short-sell 10 shares of IBX, now selling at $50 per share. a. What is your maximum possible loss? b. What happens to the maximum loss if you simultaneously place a stop- buy order at $55?
A: Theoretically, potential losses are infinite, as the potential loss grows directly with IBX's share price. The share price could keep going up, and the investor's loss exposure would continue to increase, since he/she has to buy those shares in the market. B: If the price of IBX shares goes above $55, the stop-buy order would be triggered, thereby limiting losses from the short sale. If the stop buy order can be filled at $55, the maximum loss per share is $5 (55 - 50), and the maximum total loss is $50 (10 shares x $5 per share).
Asset Allocation, Capital Allocation
Asset Allocation: Portfolio choice among broad investment classes; Refers to % stocks, % bonds, % T-bills, etc.; Determines most of portfolio's return and volatility over time. (Bigger impact than choosing stock X vs. stock Y) Capital Allocation: Most basic form of asset allocation; Choice between risky and risk-free assets Capital Allocation Line (CAL): Plot of risk-return combinations available by varying allocation between risky and risk-free assets; Plot of E(rC) against σC for different y Risk Aversion and Capital Allocation: y is an investor's preferred capital allocation; The choice of y depends on how much risk an investor is willing to take -More risk averse investors will choose smaller y and invest more in the risk-free asset. slope=Sharpe ratio Complete Portfolio: Investor's entire portfolio, including risky and risk-free assets; includes computing expected return and standard dev.
What do you think would happen to the expected return on stocks if investors perceived an increase in the volatility of stocks?
Assuming all else equal, investors will view stocks as riskier and demand a higher risk premium in order to hold the same portfolio as before. Thus, assuming the risk-free rate is the same, the expected return on stocks would be higher.
If investors become more risk averse, stock prices will _______ and expected returns will ______. A) fall; decrease B) fall; increase C) rise; decrease D) rise; increase
B Stock prices will fall as a response due to decreased demand for stocks; however, expected returns going forward will be higher, as investors will demand extra compensation to compensate for risk. Current prices and future returns have a natural inverse relationship.
You run a regression of a stock's returns versus a market index and find the following: Slope, Lower 95%=.6541 and Upper 95%=1.465 Based on the data, you know that the stock ________. A) has a true beta precisely equal to .890 B) has a true beta that is likely between .6541 and 1.465 C) has no systematic risk D) earned a positive alpha that is statistically significantly different from zero
B The true beta is likely between 0.6541 and 1.465. This is the 95% confidence interval for beta obtained from the estimated regression model. The reason choice C is incorrect is because we don't know the exact beta. Our best point estimate is 0.890, but this is estimated using a data sample and we would get a different result if you used a different time period or even a different data frequency (e.g. weekly vs. monthly returns).
An analyst forecasts that stock A will earn a rate of return of 12%, and its beta is 1.1. The market expected rate of return is 8%, and the risk-free rate is 5%. The alpha of the stock is ________. A) -1.7% B) 3.7% C) 5.5% D) 8.7%
B Expected return: 12% rs=rf+B(E(rm)-rf) rs =5%+1.1(8%-5%)=8.3% Implied alpha = 12% - 8.3% = 3.7%
A portfolio with a 25% standard deviation generated a return of 15% last year when T-bills were paying 4.5%. This portfolio had a Sharpe ratio of _________. A) .22 B) .42 C) .25 D) .6
B Explanation: (.15 - .045) / .25 = .42
Your investment has a .20 probability of earning a 30% rate of return, a .50 probability of earning a 10% rate of return, and a .30 probability of earning a -6% rate of return. What is your expected return on this investment? A) 8.9% B) 9.2% C) 11.0% D) 12.8%
B Explanation: E(r) = .20(30%) + .50(10%) + .30(-6%) = 9.2%
When first sold, Initial public offerings (IPOs) are usually ________ relative to the levels at which their prices stabilize after they begin trading in the secondary market. (Hint: underpricing should be associated with higher returns, fair pricing should be associated with average returns, and overpricing should be associated with lower returns) A) mispriced but without any particular bias (i.e. overpriced and underpriced with equal likelihood) B) underpriced C) overpriced D) correctly priced
B Explanation: IPOs are typically underpriced initially resulting in their large average first day returns. This underpricing represents an indirect cost to the issuing firm.
You have the following rates of return for a risky portfolio for several recent years: 2011: 35.23% 2012: 18.67% 2013: −9.87% 2014: 23.45% The geometric (time-weighted) average return on this investment is ________. A) 16.15% B) 15.60% C) 21.32% D) 16.87%
B [(1.3523)(1.1867)(1-.0987)(1.2345)](1/4) - 1 = .1560 or 15.60%
According to the capital asset pricing model, a security with a _________. A) negative alpha is considered a good buy B) positive alpha is considered overpriced C) positive alpha is considered underpriced D) zero alpha is considered a good buy
C Investors want to buy stocks with positive alphas, because they are effectively underpriced. Their bargain prices are what leads to positive abnormal returns.
The most appropriate measure of the riskiness of an asset held in isolation (i.e. in a one asset portfolio) is ________. A) covariance B) beta C) standard dev D) Alpha
C Standard Deviation is the most appropriate risk measure for an asset held in isolation. When evaluating the riskiness of a stock to add to a well-diversified portfolio, beta is more relevant since any firm-specific risk is irrelevant because it's diversified away.
Consider the CAPM. The risk-free rate is 6%, and the expected return on the market is 12%. What is the expected return on a stock with a beta of 1.3? A) 6.0% B) 18.0% C) 13.8% D) 21.6%
C E(rp) = rf + B(E(rm) - rf) rs = 6% + 1.3(12% - 6%) = 13.8%
If you want to measure the performance of your investment in a fund, including the timing of your purchases and redemptions, you should calculate the ________. A) arithmetic average return B) geometric average return C) dollar-weighted average return D) index return
C Explanation: Dollar-weighted returns take into account the timing of cash inflows and outflows unlike the other return measures.
An order to buy or sell a security at the current price is a ________. A) stop-loss order B) limit order C) market order D) stop-buy order
C Explanation: Market orders are executed at immediately at whatever the best available current price is in the market.
Which of the following correlation coefficients will produce the greatest diversification benefits? A) -0.6 B) 0 C) -0.9 D) 0.4
C Explanation: The lower the correlation, the greater the diversification benefits. A -0.9 correlation suggests that when one asset's price falls the other tends to go up a large majority of the time, thereby reducing overall portfolio risk.
CAPM
CAPM: Security's required rate of return is determined by its systematic risk measured by beta E(rs)=rf+Bs*(E(rm)-rf) E(rs)=expected required return on stock rf=risk free rate Bs=beta of stick E(rm)=expected return on market portfolio E(rm)-rf=market risk premium Assumptions 1)Securities markets are perfectly competitive, and equally profitable to all investors -No investor is wealthy enough to individually affect prices -All relevant information is publicly available at no cost, and all securities are publicly traded -No taxes on returns and no transaction costs -Unlimited borrowing/lending at risk-free rate -no abnormally high or low returns 2) Investors are exactly alike except for initial wealth and risk aversion -All investors plan for single-period horizon -All investors are rational, mean-variance (standard dev) optimizers -Investors use the same inputs and consider identical portfolio opportunity sets Hypothetical Equilibrium -All investors choose to hold the market portfolio (M) -The market portfolio includes all assets (not just stocks) -The market portfolio (M) is on the efficient frontier and is the optimal risky portfolio (tangent point) -The risk premium on the market portfolio is a function of both: the variance of the market portfolio and risk aversion of the average investor -When stocks are riskier and/or investors are less willing to accept risk, higher expected returns are required -The risk premium on individual assets is Proportional to the risk premium on the market portfolio, proportional to the security's beta (i.e. systematic risk)
What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 12%? (Multiple Choice) a. 12% b. More than 12% c. Cannot be determined without the risk-free rate.
Choice A. It's expected return should be exactly the same as the market's, because its beta is the same as the market's beta. The CAPM suggests beta determines variation in expected returns. if Beta=1 then it equals E(r)
A market order has (multiple choice): A. Price uncertainty but not execution uncertainty B. Both price uncertainty and execution uncertainty C. Execution uncertainty but not price uncertainty
Choice A. Market orders instruct the broker to buy or sell a security at the best available market price; however, the investor does not know with certainty what price the trade will be executed at. In contrast, with a limit order the investor specifies the price he/she is willing to transact at (price certainty), but the trade may not be completed (execution uncertainty) if that price cannot be obtained.
You estimate a regression of a stock's returns versus a stock market index and find the following: Lower 95%, slope=0.6541 Upper 95%, slope=1.465 Based on the data, you know that the stock: a. Earned a positive alpha that is statistically significantly different from zero b. Has a true beta that is exactly equal to .890 c. Has a beta that is likely to be something between .6541 and 1.465 d. Has no systematic risk
Choice C is correct, because the confidence interval suggests we are 95% sure that the true beta is between 0.6541 and 1.465. We rely on a selected sample of data to estimate its value; therefore, we never know the exact value and our estimate will vary depending on the choices we make during the estimation procedure. This is why B is incorrect.
According to the separation property, portfolio choice can be separated into two independent tasks consisting of ________ and ________. A) 1. Identifying all investor imposed constraints; 2. identifying the set of securities that satisfies the investor's constraints and offers the best risk-return trade-offs B) 1. identifying the investor's degree of risk aversion; 2. choosing securities from industry groups that are consistent with the investor's risk profile C) 1. choosing which risky assets an investor prefers according to the investor's risk- aversion level; 2. minimizing the CAL by lending at the risk-free rate D) 1. identifying the optimal risky portfolio; 2. constructing a complete portfolio consisting of the risk-free asset and the optimal risky portfolio based on the investor's degree of risk aversion
D An important result related to the Optimal Risky Portfolio is that assuming equal data inputs, all investors will find the same optimal risky portfolio, and then construct their complete portfolio by investing part in the optimal risky portfolio and part in the risk-free asset. Their exact asset allocation will depend on their risk aversion.
Your investment has a .40 probability of earning a 15% rate of return, a .50 probability of earning a 10% rate of return, and a .10 probability of earning a -10% rate of return. What is the standard deviation of this investment? (Hint: Expected return = 10%) A) 7.59% B) 5.14% C) 8.66% D) 7.07%
D E(r) = .40(15%) + .50(10%) + .10(-10%) = 10% Var(r) = .40(15-10)2 + .50(10-10)2 + .10(-10-10)2 = 50 %2 SD(r) = sqrt(50) = 7.07%
An investor places 70% of her wealth in a risky asset with an expected rate of return of 15% and a standard deviation of 22.4%, and she invests the other 30% in a Treasury bill that pays 5%. Her portfolio's expected rate of return and standard deviation are ________ and ________ respectively. A) 10%; 6.7% B) 10%; 35% C) 12%; 22.4% D) 12%; 15.7%
D Explanation: E(r) = .7(15%) + .3(5%) = 12% SD(r) = .7*(22.4%) = 15.7%
Trading Mechanisms
Dealer markets: Over-the-counter (OTC) market- Informal network of brokers/dealers who negotiate securities sales Electronic communication networks (ECNs): Computer networks that allow direct trading without market makers Specialist markets: Specialist- Makes market in shares of one or more firms; maintains "fair and orderly market" by dealing personally (NASDAQ) Algorithmic Trading: Use of computer programs to make rapid trading decisions, Estimated to account for more than 50% of equity trading in U.S. High-frequency trading: Uses computer programs to make very rapid trading decisions in order to compete for very small profits
Suppose your timing was good last year. You invested more in your portfolio right before prices went up, and you sold right before prices went down. In calculating historical performance measures of arithmetic, geometric, and dollar-weighted average returns, which one do you expect to be the highest? Explain why.
Dollar-weighted average return would likely be the highest, since it takes into account the timing of the cash flows by placing greater weight on periods when more money is invested and less weight on periods when not as much is invested. Since your timing was good in this example, this works to increase the dollar-weighted average.
In forming a portfolio of two risky assets, what must be true of the correlation coefficient between their returns if there are to be gains from diversification?
If the correlation coefficient is below 1.0 (i.e. the returns do not have a perfect positive correlation), the portfolio will benefit from diversification because the returns will not move perfectly together. The portfolio standard deviation will be less than a weighted average of the individual asset standard deviations. Additionally, the lower the correlation coefficient, the greater the diversification benefit will be.
Separation Property
Implies portfolio choice is "separated" into two tasks: 1)Determination of optimal risky portfolio 2)Choice of allocation between risky portfolio and risk-free asset. Separation Property Implications: -Few portfolios are needed to serve a large set of clients -In the absence of investor constraints (e.g. short sale restrictions, tax considerations, social concerns), all investors would have the same optimal portfolio
Investment Opportunity Set
Investment opportunity set: the set of all attainable risk-return combinations -An Investor's final portfolio choice will depend on risk preferences -A low return, low risk asset is not clearly better or worse than a high return, high risk asset -By plotting all the expected return, standard deviation pairs, we can graph the full set of investment opportunities. -For lower correlations, the opportunity set shifts up (higher expected return) and to the left (lower standard deviation). -diversification benefits/investment opportunities increase as correlation decreases -Better curves lie further to the top left of the graph (i.e. higher expected return and lower standard deviation)
When adding a risky asset to a portfolio of many risky assets, which property of the asset is more important, its standard deviation or its covariance with the other assets? Explain.
Its covariance with the other assets is more important, because diversification benefits and the amount of risk reduction is determined by correlations with other assets. In a well-diversified portfolio this is the largest determinant of overall risk. covariance matters when computing overall risk
Why have average trade sizes declined in recent years?
Many large investors seek anonymity to hide their intentions to buy/sell large quantities. Large block trades attract the attention of other traders, which could result in adverse price movements (e.g. stock price becoming lower before the investor can sell all of his/her shares). By splitting large transactions into smaller trades, investors are better able to retain a degree of anonymity.
How do margin trades magnify both the upside potential and downside risk of an investment portfolio?
Margin is a type of leverage that allows investors to post only a portion of the value of the security they purchase and borrow the rest. Thus, when the price of the security rises or falls, the gain or loss represents a much higher percentage relative to the actual money invested.
Margin Trading
Margin: Securities purchased where some of the funds are borrowed from the broker, Net worth of investor's account Initial Margin Requirement (IMR) IMR = Minimum % initial investor equity 1 − IMR = Maximum % amount investor can borrow Maintenance Margin Requirement (MMR): Minimum percent equity before additional funds must be put into account, Exchanges mandate a minimum of 25% Margin Call: Notification from broker that additional funds must be deposited or position will be liquidated -If (market val-amount borrowed)/market value is less than or equal to MMR, margin call occurs
Diversification and Portfolio Risk
Market/Systematic/Nondiversifiable Risk: Risk factors common to whole economy Examples: business cycle, interest rates, inflation FirmSpecific/Nonsystematic/Diversifiable Risk: Risk that can be eliminated by diversification Examples: lawsuits, success in R&D, new product launch
Is the following scenario possible? Explain. 2 portfolios: A E(r)=12%, B=1.3 B E(r)=20%, B=1.1
Not possible. Stock A has a higher beta but a lower expected return, which is a violation of the CAPM. higher B=higher E(r)
Optimal Risky Portfolio
Optimal Risky Portfolio: The best combination of risky assets resulting in the highest Sharpe ratio; Tangency point on risky asset investment opportunity set Slope of Capital Allocation Line (CAL) is the Sharpe Ratio of the Risky Portfolio Adding a risk-free asset: Improves the investment opportunity set; We'll see the resulting opportunity set is a straight line Investors' decisions can be broken down into two parts: 1)Find the risky portfolio offering the best risk-return tradeoff 2)Choose allocation between this optimal risky portfolio and risk-free asset (choice depends on risk aversion) ***Optimal portfolio CAL is tangent to efficient frontier
Price Contingent Orders
Price Falls Below the Limit: buy-->Limit buy order sell-->Stop loss order Price Rises Above the Limit: buy-->Stop buy order sell-->Limit sell order A stop order is a trade that is not to be executed unless the stock price falls to a certain level in order to limit potential losses when prices are falling. A limit sell order says to sell the stock if and only if the price rises to at least a certain level (i.e. the investor's limit price). A market order directs the broker to buy or sell at whatever price is available in the market.
Sharpe (Reward to Volatility) Ratio
Ratio of portfolio risk premium to standard deviation S=𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚/𝑆𝐷 𝑜𝑓𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑒𝑥𝑐𝑒𝑠𝑠 𝑟𝑒𝑡𝑢𝑟𝑛 portfolio risk premium=E(rp)-rf Mean-Variance Analysis:Ranking portfolios by Sharpe ratios, Evaluates which portfolios offer best risk-return tradeoff -Want a high ratio (higher reward to lower volatility) -numerator is reward and denominator is risk, want higher numerator and smaller denominators
CAPM and Index Models (ctd)
Regression estimation results: Produces an estimate of the asset's security characteristic line (i.e. alpha, beta) How confident should we be in the results? To answer this we can look at: 1) t-statistic: T-tests are used to test a hypothesis of whether 2 values are significantly different from one anothe; t=(estimated val-hypothesis val)/standard error of estimate -When an estimate is 2 or more standard deviations away from 0, the value is extreme enough to be unlikely to occur by chance. (e.g. can reject 𝛼=0), more than 2 standard deviations away from 0 then we are confident 2) p-value: p-value less than 0.05 is considered sufficient to say an estimate is statistically significant, true alpha=0 3) confidence interval: example) Google's alpha Confidence interval: (-1.74, 3.49) ex) 95% confidence interval (.3, 1.1) <--0 is not included so we have true confidence that the alpha is higher than that Results indicate 95% confidence that the true alpha is between -1.74 and 3.49 (rounded values) Thus, Google's true alpha could be 0, since it is within the interval
Risk Premiums and Risk Aversion
Risk-free rate: Rate of return that can be earned with certainty (e.g. return on T-bills)—assume default rate is 0 Risk premium: Expected return in excess of the return on risk-free securities Excess return: Actual return in excess of the risk-free rate, if lose % return then excess return is negative but expected return is still positive Risk aversion: Reluctance to accept risk
Short Selling
Short sale: sale of shares not owned by an investor but borrowed through a broker and returned later -Borrow stock from broker and post required margin -Broker sells stock and deposits proceeds in your account (these funds remain in the account) -Buy stock to close out (i.e. "cover") position Long position: Buy first, sell later Bullish (betting on price to rise) Short position: Sell first, buy later Bearish (betting on price to fall) Required initial margin: Usually 50%, More for low-priced stocks Investor is liable for any cash flows E.g. Dividend on stock
CAPM and Index Models
Simple CAPM derivation: -Assume all assets earn the same risk premium per unit of systematic risk (beta) -Now consider the ratio of risk premium to risk for the market portfolio and stock S Simple CAPM derivation: -Assume all assets earn the same risk premium per unit of systematic risk (beta) Index Model: used to test the CAPM -The theoretical market portfolio is replaced with an index (e.g. S&P 500) -Actual return outcomes are used, not expected returns -Goal: see if differences in beta explain differences in average returns Index Regression Equation: rit-rft=ai+Bi(rat-rft)+eit rit=holding period return ("of asset i in period t") rft=risk-free rate ai= alpha; security characteristic line intercept Bi= beta; security characteristic line slope rmt= index return eit= firm specific effects Security Characteristic Line (SCL) - plot of security's expected excess returns as a function of market excess returns -This best fit line tells us alpha, beta, and whether firm specific risk is high or low
Suppose you've estimated that the fifth-percentile value-at-risk of a portfolio is -30%. Now you wish to estimate the portfolio's first-percentile VaR (the value below which lie 1% of the returns). Will the 1% VaR be greater or less than -30%?
The 1% VaR will be less than -30%. As the percentile of a return declines so does the value of that return. Thus, a 1st percentile probability will produce a smaller VaR than a 5th percentile probability. Returns lower than the 1% VaR represent the worst 1% of returns.
Efficient Frontier
graph of the set of portfolios that offer the maximum expected return for each level of risk (above CAL) -Maximum risk premium for any level of standard deviation, or -Minimum standard deviation for any level of risk premium
CAPM ctd.
oBe able to Draw and Label Security Market Line (graph of the CAPM) Individual Security Returns -Only systematic risk matters to investors -Beta measures systematic risk only, unlike standard deviation -As a result, risk premiums are proportional to beta -Diversifiable risk does not earn a risk premium, because investors can diversify it away without sacrificing return -Capm says that only have high return if beta is high (not standard deviation) -Beta is how much market goes up and down, systematic risk -Standard deviation is how volatile returns are, total risk (systematic and diversifiable) -The Security Market Line (SML): Graphical representation of the expected return-beta relationship of the CAPM -Alpha: Rate of return on a security in excess of that predicted by an equilibrium model (e.g. CAPM), Reflected by how far points lie above or below the SML
