Concepts Flashcards
What are the three portfolio parameters that has to be adressed in setting up a portfolio?
- Asset allocation
- Strategic allocation: Choice between different asset classes (bonds, stocks, derivatives etc.)
- Tactical allocation: Deviation from weights invested in different asset classes compared to strategic allocation - Choice of portfolio management
- Active portfolio management: Actively searching for “undervalued” assets
- Passive portfolio management: Buy-and-hold approach - Security selection (choice of security within an asset class)
What are the broad categories of “Players” on the financial markets? Main parameters of them?
Companies:
- Are net borrowers
- Raise capital in the security markets (usually common stock and bonds) to invest in real assets.
Households
− Are net savers
Governments
− Can be net savers (e.g., Norway, Singapore) or net borrowers (which is usually the case)
− Borrow funds to invest in infrastructure (streets, bridges, universities etc.)
Financial intermediaries
− They role is to match supply and demand of capital
Financial intermediaries perform a transformation function with respect to?
Liquidity
Maturity
Size
Risk
Financial assets: What is “Money market”? Who invests in them?
- Short-term (
Who issue bonds?
− Governments or related agencies (government bonds, municipal bonds…)
− Companies (corporate bonds)
− Special purpose vehicles (asset backed securities)
Common stock, what are the two main characteristics?
− Residual claim: Holders receive what is left over in the firm after every other claim is settled
− Limited liability: Holders are not liable with their personal wealth for the firm’s obligation
Preferred stock, what is its similarities to debt?
- Holder receives a fixed payment each year → Bond with infinite maturity
- Holder has no voting right
- Are sometimes also callable or convertible (Which bonds also can be if an option is attached)
Preferred stock, what is its similarities to equity? What are its differences to common stock?
Similarities
- The board of directors can decide whether to pay a dividend or not
- Costs for dividends are not deductible on firm level (as are interest payments)
Differences:
- If not: Dividend usually accumulates
- No dividend can be paid out to common stock holders until cumulated divided to preferred stock is paid out
How does equity indices differ?
Weighting of components:
- Price-weighted index (DJIA)
- Value-weighted index (S&P500)
- Equally-weighted index
Treatment of dividends
- Price index (DJIA, FTSE100)
- Performance index, also known as total return index (DAX30)
Asymmetric derivatives, examples and parameters
Call and Put options
- Gives the buyer the right to buy (call) or sell (put) an asset
- For a predefined price (exercise price)
- At a or before a predefined date
- The buyer of the option has the right, but not the obligation to exercise the option
Symmetric derivatives, examples and parameters
Futures and swaps
- Buyer (long) and seller (short) agree to exchange an asset
- For a predefined price
- At a predefined date
Underwriter
Usually investment bank(s), help an issuing firm preparing the prospectus, marketing the securities, and they also track the stock or the bond after the issue
Seasoned equity offering
A subsequent offering of equity by a firm
Public offering
Firms that offer securities to the general public
Private placement
Securities offering sold to a few institutional investors
Direct search markets
− Seller and buyers search each other individually
− Least organized market, sporadic participation, nonstandard goods
− Example: WG-gesucht.de
Brokered markets
− Brokers offer search services to buyers and sellers to find each other
− Example: Primary stock and bond markets, real estate market
Dealer markets
− Dealers buy assets on their own account and resell them at higher prices (the “spread”)
− Requires market activity
− Example: Some bond and equity markets
Auction markets
− Buyers and sellers meet at one place and trade; most integrated form of trading
− Example: Most stock and bond markets, derivative markets trade as continuous auctions
Market orders
− Buy or sell order that is executed immediately at the current market price
− In securities that are rarely traded (“low liquidity”) these trades can be expensive since the price is determined on the market
What is price-contingent orders? Advantage and disadvantage?
− Limit orders:
Buy or sell order that is executed if the prices crosses a certain threshold
− Stop orders:
Similar to limit orders, but aim at preventing losses
− Disadvantage: Questionable whether order will (ever) be executed (immediacy)
− Advantage: Transaction price known beforehand
What happens if investors post limit orders?
They get cumulated in a limit order book where the current limit orders are visible (Order book depth)
Buying on margin
When purchasing securities, investors usually have access to debt financing for the purchase transaction (usually offered by the broker)
− The buyer has to provide the margin
− The broker lends the remainder to the investor and charges him interest and fees; the securities bought serves as collateral for the loan
Short sales, what is it and how does it work in practice?
An asset is sold before it is bought and it allows investors to participate in declining asset prices
In practice, an investor would ask his broker to sell a security short. The broker would lend the security owned by another client to the investor, who would sell it. The position is closed when the investor returns the security to the broker by buying it back on the market.
Pro banning short-sales
− Short-sellers bet on falling prices by spreading rumors, thereby taking companies down that would otherwise survive − Sort-sellers gain by betting on other individual’s misfortune − Short-sales manipulate prices
Contra banning short-sales
− Short sellers correct prices even before bubbles can occur
→ Housing bubble occurred because short selling in houses is impossible
− Practically difficult to stop short sales anyway
The real interest rates are determined by the following factors
− Supply of capital (by households)
− Demand of capital (by companies and the government)
− Government actions (central bank interventions)
Why does the supply curve slope upward with increasing real interest rates?
- Because households are willing to supply more capital by postponing current consumption to the future.
Why is the demand curve downward sloping with increasing real interest rates?
Because companies and the government are willing to borrow more money if the cost of borrowing is lower, i.e. it is more expensive for them and therefore they do not borrow
What can governmental action do in terms of the interest rate graph?
Governmental action can shift both the demand and the supply function
What does it mean with the “inflation penalty” in terms of taxes?
- Taxes payable are determined on nominal income and an investor‘s tax rate (𝑡𝑡), while investors earn real rates of return.
- As income grows due to inflation, individuals are pushed into higher tax brackets in a progressive tax system.
- Even if this is recognized in the tax code (which is not, in most countries), individuals loose purchasing power:
Annual percentage rates (APR)
− Annual interest rate paid
− Does not reflect compounding of interest paid
Effective annual rates (EAR)
− Annual interest rate reflecting compounding of interest paid
→ More interest payments in a given year result increase the effective interest rate
Skewness
Statistical measurement that shows whether a distribution is symmetric or skewed
A distribution with positive skewness is skewed to the right, while a distribution with negative skewness is skewed to the left
Kurtosis
- Measures whether a distribution shows “fat tails”
- A distribution with kurtosis measure > 0 has “fat tails”
→Intuition: “Extreme” realizations are more likely to occur
Various methods allow to test whether a given distribution satisfies the assumption of normal distribution
− Chi-squares-test
− Kolmogorow-Smirnow-test
− Shapiro-Wilk-test
− Maximimum-likelyhood-test
− Shapiro-Wilk-test
- High accuracy in small samples, but sensitive to outliers
Hypotheses:
H0: Population is normally distributed.
H1: Population is not normally distributed.
What are the normal distribution assumptions in finance? Are they correct?
- > In Finance, we usually assume that the log-returns are distributed according to normal distribution
- > There is evidence that returns are not normally distributed (Existence of skewness and kurtosis)
Risk-averse
An investor prefers a risk free investment over a risky investment with the same expected return
→ An investor demands a premium for taking risk
Risk-neutral
An investor compares two investments solely on the basis of expected returns, neglecting risk
→ An investor does not demand a premium for taking risk
Risk-loving
An investor prefers a risky investment over a risk free investment with the same expected return
→ An investor is willing to pay a premium for taking risk
Quadratic utility
- We assume that investors can assign a utility to an investment to evaluate and compare investments only based on expected return and risk
- Under quadratic utility, the utility can be interpreted as the certainty equivalent
What are the implications of “A”, i.e. aversion parameter under quadratic utility
- It follows that the higher the risk aversion (higher 𝐴), the steeper are the indifference curves
- Intuition: Investors with higher risk aversion require a higher premium for a marginal risk increase
Utility maximizing portfolio
- An investor choses the combination of investments in the risky portfolio and the risk-free asset that maximize his utility
- We can identify the portfolio that touches the indifference curve with the highest utility
Insurance principle
By increasing the number of stocks in the portfolio to infinity, we reduce the influence of firm-specific risk-factors to zero
Systematic risk
(also called market risk, non-diversifiable risk)→ Risk that remains in every portfolio
Unsystematic risk
(also called unique risk, firm-specific risk, non-systematic risk, or diversifiable risk)→ Risk that can be eliminated
What happens if the returns show a perfect positive correlation?
In this case both asset prices move together
→ Diversification bears no benefit.
What happens if the returns show a perfect negative correlation?
In this case both asset prices move exactly in the opposite direction
→ Diversification works perfectly
The CAL (also known as the Sharpe ratio)
- Measures the slope of the return-risk relation of a given portfolio
- We can optimize the risk/return tradeoff of our investment by maximizing the slope of the CAL:
The only choice an investor makes in terms of optimal complete portfolio?
Since everyone holds the optimal risky portfolio
→ The only choice an investor makes is how much of his wealth to invest risky and how much to invest risk-free depending on individual investors’ risk preferences
The Markowitz portfolio, three main characteristics
• Minimum variance frontier:
All portfolios with the lowest standard deviation for a given expected return mark the minimum-variance frontier
• The global minimum variance portfolio:
Is the portfolio with the lowest standard deviation possible
• Efficient frontier:
All portfolios with the highest return for a given standard deviation mark the efficient frontier
What happens when the average correlation between assets is zero? Is it realistic?
- Firm-specific risk can be diversified away by increasing the number of stocks and portfolio risk becomes zero
- It is NOT realistic since usuallu fundamental factors influence all stock returns in a similar way, i.e. the portfolio variance remains positive
Investors require a risk-premium for securities with? Why?
Higher correlations, and NOT for securities with higher standard deviations
-> It is correlation that drives portfolio variance NOT the asset variances itself
Idea of single-factor model
− Simplify description of risk, allowing for a smaller but consistent set of estimates of risk and risk premium parameters
− Positive covariances among securities are driven by some common economic factors (business cycles, interest rates, cost of natural resources etc.) that affect most firms, but to varying degree
− Decomposing overall portfolio risk into firm-specific and systematic risk vastly simplifies estimation
The Markowitz optimization has several drawbacks
− Number of input parameters is high (We need to measure correlation between EVERY asset)
− Incorrectly specified parameters lead to suboptimal portfolio composition
Advantages of single-factor model compared to Markowitz
− Number of input parameters necessary is substantially reduced
− Practically: Under Markowitz, analysts would have to come up with covariances for each pair of firms. Now: Analysts can focus on one company (or one industry) and provide their management team with one figure: the beta
− Separation of market-wide and firm/industry-specific analysis adds value
Disadvantages of single-factor model compared to Markowitz
− Simplification might reduce accuracy of estimation and thereby reduce accuracy of selection (e.g., error terms for certain securities might be correlated in the real world)
− Securities are treated as completely different investments, while some might be substitutes
Markowitz optimization
Estimation of the optimal risky portfolio using full information on the returns, variances and covariances of all securities available for portfolio selection.
→ Precise, but exhausting procedure that often requires substantial computing power.
Optimization using index models
Procedure is facilitated by reducing the number of parameters, first and foremost substituting the number of covariances with a sensitivity to a common factor.
→ The number of parameters is reduced at the cost of precision. However, the estimated risk-return-profiles usually do not differ substantially. What differs, however, is the portfolio weights assigned to different securities.
The basic assumptions of the CAPM are:
Frictionless markets:
- Investors are price takers
- Investors can borrow and lend at the same rf rate
- Investors pay no taxes and no transaction costs
Investor behaviour:
- All investors are mean-variance optimizers (Use Markowitz to optimize)
- All investors plan for ONE holding period
- All investors analyze the same way and have the same input factors -> homogenous expectations
All investors are equal except wealth and risk preference
What does it imply when the market portfolio is efficient
It has to hold that the marginal return to marginal risk contribution is the same for any given security and equals the slope of the capital market line
Let‘s assume the stock market is not in equilibrium and the current stock price of company XYZ is too low, what happens according to CAPM?
→ The expected return of this asset is too high (since the current price is too low), while the risk profile remains the same
→ All investors recognize this pattern and rebalance their portfolios accordingly
→ Due to increased demand for the stock, the price increases again until the market is back in equilibrium
→ This happens with all assets continuously so that the prices are always in equilibrium and the market portfolio comprises all assets
Name three CAPM implications
- All investors optimize (with Markowitz) by using the same input parameters. Every investor comes up with the market portfolio as her optimal risky portfolio. Allocates according to wealth and risk preferences.
- The market portfolio will be on the efficient frontier. The capital allocation line (CAL) will become the capital market line (CML). This is the best attainable capital allocation among risky investments into the market portfolio and risk free investments in the entire economy.
- The value of the market portfolio is the aggregate value of ALL traded securities (or the wealth of the entire economy): The relative weight of an asset is the value of the asset scaled by the value of the market portfolio. Note: This is also the weight of the asset in each individual investor’s portfolio!
Mutual fund theorem
In the simple CAPM world, the market portfolio M is the efficient portfolio
This is called the mutual fund theorem: Portfolio selection can be separated into two parts:
- Creation of a mutual fund that represents the market portfolio (technical problem)
- Personal allocation of capital by investors into the market index mutual fund and into the risk free asset
Investors could stop with security analysis by simply holding the market portfolio
In the CAPM-world, an asset’s expected return is determined by?
the return and the risk it contributes to the market portfolio
In the CAPM-world, the covariance of an asset with the market portfolio is the?
Sum of the covariances of the asset with all other assets in the market portfolio
What is the Beta?
Beta measures the co-movement of an asset and the market: If a stock has a beta of −0.8, we would expect that the stock price falls by −0.8%if the market were to move by +1.0%.
The Security Market Line (SML)
- Relates individual asset risk to required returns
- The market portfolio as an asset itself lies on the SML. with a Beta of 1
- All securities lie on the SML, at least in the long-run
- Undervalued (Overvalued) assets lie above (Below) SML since they have more (less) return considering their risk and the distance to the SML is the alpha value, which is positive for undervalued assets
- The SML shows the risk-premium of a single asset as a function of asset risk.
- To assess “risk”, we are interested in estimating the risk
contribution of an asset to the market portfolio. - We can thus use the SML as a benchmark measure for
investment performance.
The CAPM is often used for practical applications, including
− Portfolio management→ find positive alpha stocks
− Performance measurement→ a skilled fund manager should be able to generate positive alphas
− Investment decisions and project evaluation→ determine the required rate of return for a given project using a project’s beta (so-called internal rate of return (IRR) or hurdle rate)
− Security and company valuation→ determine the required rate of return for a given asset using the asset’s beta
− Regulation in US and Europe
Can we test the CAPM empirically? We can test whether?
− “the market portfolio” is mean-variance efficient
− stocks with higher risk (beta) have higher expected returns (not really)
− unsystematic risk affects expected returns (not really)
− the risk return relation is linear
Main problem for all CAPM tests? How is it solved?
- The CAPM uses expected returns, which are unobservable.
- We use observed returns
“Roll’s critique”
− We do not observe the “true” market portfolio since we do not observe all possible investments (e.g., human capital) →We cannot test whether the market portfolio is an efficient investment
− Since we cannot observe the market portfolio, most tests aim at the expected return –beta relationship: These tests do not work out well either, since low-beta stocks have a positive alpha (and vice versa)
A number of econometric issues complicate empirical testing of the CAPM, which are these?
− Biases in estimation (e.g., Miller and Scholes, 1972): The tests even fail for a hypothetical portfolio that is in accordance with the CAPM!
− Betas are in reality time-variant (due to structural breaks)
− Event if an asset is traded, betas for some assets are often miss-specified (e.g., for thinly traded stocks and bonds)
We cannot fully explain the real world using the CAPM, in addition to more technical issues, this might also be due to failure of
− the data available,
− the proxy for the market portfolio and/or
− statistical miss specification.
Why is the CAPM so generally accepted?
− Compelling model: Separating firm-specific risk factors from market-wide risk factors is intuitive
− The number of investment funds that employ smart people, but fail to beat the market portfolio consistently is surprisingly small given the lack of empirical evidence supporting the market portfolio as the “best” investment.
− Other available models are often only more complicated, but do not yield better results (see next lecture)
Reasons for CAPM extensions? What is the downside?
− Gaining predictive accuracy and relaxing restrictive assumptions
− Overcome (some of the) shortcomings
− But: extensions usually lead to greater complexity
What types of extensions to CAPM are there?
− Incorporate labor income and non-traded assets (esp. human capital and private businesses),
− Cover multi-periods (Merton, 1973: Intertemporal CAPM or ICAPM),
− Incorporate current savings (=future consumption) versus current consumption (Consumption-based CAPM),
− Cover liquidity effects and costly trading,
− Include other priced factors (Small-minus-big, High-minus-low, momentum)
Why should investors search for alpha?
− All investors maximize absolute returns of their holdings
− Alpha can compensate for low returns achieved by the market (beta)
− Markets are not fully efficient, generating alpha might thus be possible
Why should investors neglect alpha?
− For each investor achieving a positive alpha, another investor has to suffer (zero-sum game)
− Searching for alpha creates cost: After accounting for search costs, searching for alpha is not profitable
− More than 10,000 hedge funds search for alpha; it seems unrealistic to beat them all over many years!
What is the implication of risk-premium in SML?
→ An investor is only compensated with a risk-premium for exposure to systematic risk, not for holding firm-specific risk
Idea behind the APT
- Security returns can be described by a factor model,
- A sufficient number of securities exists that allows diversifying idiosyncratic risk, and
- Well-functioning (efficient) markets do not allow arbitrage opportunities to persist.
→ Securities are priced based on their factor-exposure and the market prices for factor exposure are based on arbitrage-free pricing
Definition of arbitrage
− Earning risk-free profits from security misspricing without making a net investment
− “Law of one price”: Two assets that are equivalent in all important aspects should have the same market price.
− An arbitrage strategy usually involves simultaneous buying (the cheaper security) and selling (the expensive security) in order to profit from price discrepancies.
(Example: A stock that sells on NYSE for $95 and for $93 on NASDAQ allows a “free-lunch” of $2.)
Difference in APT compared to CAPM in terms of arbitrage
− It is sufficient that only a few arbitrageurs recognize an arbitrage opportunity and profit from it by engaging in arbitrage trading on a large scale (CAPM ALL investors rebalance)
→ The assumption is less strict compared to the CAPM (but we will later see that it leaves the possibility that a few single securities are mispriced)
Name 5 comparisons of CAPM and APT
- Both models use and show the difference between diversifiable and non-diversifiable risk: The former does not require a premium, the latter does.
- In the APT world, a few investors are sufficient to bring market prices back into equilibrium, while in the CAPM world, all investors rebalance portfolios if securities are misspriced.
• The APT does not rely on the construction of the market portfolio (which is one of the main problems for the CAPM in practice!); every well-diversified portfolio can be used.
- In the APT world, not all securities necessary lie on the SML. In the CAPM, all securities lie on the SML (at least in the long run).
- Both models are useful for security valuation, investment decisions, and performance measurement.
Main shortcoming of APT
Which factors to use!
We could introduce as much factors as we want, but ideally, we want:
- A reasonable number of factors that are meaningful and
− Sufficiently explain security returns.
Chen, Roll, and Ross (1986) empirical testing of APT factors showed
- Significant positive influence of change in industrial production
- Significant negative influence of change in unexpected inflation
- Significant positive influence of risk premium
- Equally-weighted market return and value-weighted market return turns out insignificant
The Fama-French Three-Factor Model, APT approach
- Use firm characteristics that represent relevant sources of systematic risk
- Chose factors that predict average returns
- Rm is the market return, capturing macroeconomic factors (CAPM)
- SMB is “Small minus Big”, i.e. the excess return of a portfolio of small firms stocks over a portfolio of large firms stocks
- HML is “High minus Low”, i.e. the excess return of a portfolio of high book-to-market firms over a portfolio of low book-to-market firms
The Carhart Model APT
- Carhart adds another anomaly to the Fama-French three factor model: Momentum
- Portfolios with “winner stocks” tend to perform well in the future, while “loser stocks” tend to perform badly in the future
What happened in the 50s when you got computational power
→ It seemed that prices do not follow certain “patterns”; instead, results suggested that market prices follow a “random walk”
Some researchers concluded that markets behave “erratic” and follow “animal spirits”
→ But: It became apparent that random price movements indicate well-functioning (so-called “efficient”) markets
When does prices change in EMH?
→ Prices change only when new information becomes available
→ By definition, “new information” is information that is new for investors and therefore unexpected by the market
→ “New information” hits the market randomly
→ From the outside, it might seem that market prices are random, but it is new information that becomes available randomly (so-called random walk of stock prices)
Grossman and Stiglitz(1980)
− Investors will have an incentive to spend time and resources on information collection
→ Uncover something that has been overlooked by the market
− In market equilibrium, information gathering by investors should yield a positive return that is independent from market risk factors
What is the underlying reason to market efficiency? What does it imply?
→ Competition among investors is the source of market efficiency
→ Not all markets are efficient to the same extent! Markets not under strong public observation offer more possibilities to possess more information than the average market participant
Jensen (1978) EMH definition:
“A market is efficient with respect to information set Ωt if it is impossible to make economic profits by trading on the basis of information set Ωt.”
Malkiel(1992) EMH definition:
“A capital market is said to be efficient if it fully and correctly reflects ALL RELEVANT INFORMATION in determining security prices. Formally, the market is said to be efficient with respect to SOME INFORMATION set, Ωt, if security prices would be unaffected by revealing that information to all participants. Moreover, efficiency with respect to an information set, Ωt, implies that it is impossible to make economic profits by trading on the basis of Ωt.”
Bodie, Kane, and Markus (2011) EMH definition:
“Stock prices fully and accurately reflect PUBLICLY AVAILABLE INFORMATION. Once information becomes available, market participants analyze it. Competition assures that prices reflect information.”
Weak form of market efficiency (In terms of available information)
Security prices only contain information available from past security trading (past prices, returns, trading volume, short interest etc.)
Semi-strong form of market efficiency (In terms of available information)
Security prices contain all publicly available information (fundamental data such as accounting data, patents possessed, CEO skills, analyst forecasts etc.)
Strong form of market efficiency (In terms of available information)
Security prices contain all available information (also information that is not publicly available such as future product launches and proprietary R&D development stages etc.)
Technical analysis
→ Chartists undertake technical analysis by studying past stock prices and past responses to new information
→ They try to identify recursive patterns (e.g. resistance levels / support levels)
- According to the weak form EMH, chart analysis is useless: Analyzing past price and volume movements and comparing
Support lines
Price barrier at which the demand is strong enough to prevent prices from falling further
Resistance lines
Price barrier at which the supply is strong enough to prevent prices from rising further
Trend lines
Uptrend lines: Net demand increases
even as prices increase
→ Indication that supply is lower than
demand of a stock
Downtrend lines: Net supply increases even as prices decrease→ Indication that demand is lower than supply of a stock
Fundamental Analysis
- Rather than analyzing past trading patterns, investors can analyze firm prospects (risk, market growth etc.) to come up with a better assessment of the stock price
→ Fundamental analysts try to estimate the future payments to shareholders in order to estimate the fair stock price - According to the semi-strong form EMH, fundamental analysis is useless: No analyst will beat a rival analyst by analyzing publicly available firm information ((annual reports etc.) since all analysts rely on the same information
Active vs. Passive portfolio management and EMH
According to the semi-strong form EMH, active portfolio management is useless: A passive strategy yields the same return (after trading costs) since all investors rely on the same set of publicly available information
Portfolio Management in efficient markets
Even if prices are fair and all currently available public information is contained in security prices, investor still have to
- Set up a well-diversified portfolio of risky assets to be immune to firm-specific shocks
- Set up a portfolio that suits their needs (i.e., chose between risky portfolio and risk-free investment, payouts at certain points in time etc.)
=> I.e. you cannot let a monkey decide
The main purpose of security markets
The allocation of funds from investors (those in possession of excess funds) to those wanting to undertake investments into real assets (those in need of funds)
Deviations from market efficiency will cause?
→ Deviations from market efficiency will cause substantial deadweight costs for society due to miss-allocation of funds
Example: Dot-com bubble, where the prospects of communication and internet companies was overestimated, leading to a substantial miss-allocation of capital
Momentum
- Price-Momentum:
Stocks with higher returns in the past continue to perform better - Profit-Momentum:
Stock prices follow the expectations of bank analysts - A number of studies found that so-called Momentum strategies are profitable, which clearly contradicts the weak form EMH
- Other studies (De Bondt and Thaler 1985) show the other way around, conclusion: → Short-run over-reaction to news leads to a long-run reversal
A major problem in Semi-Strong form tests
A major problem in all these tests is that we test for a joint hypothesis: We test at the same time whether
− markets are semi-strong efficient and
− the risk-adjustment made is correct
Anomalies
- Abnormal risk-adjusted return found by e.g. fundamental analysts
Their existence is not in accordance with the EMH in two aspects:
- Profiting from fundamental analysis violates the EMH in the semi-strong form
- Well-known anomalies should vanish after they become public, which violates the EMH in the weak-form
Two possible explanations for a profitable trading strategy
→ If we find a trading strategy to be profitable after accounting for risk, it might be:
- That markets are inefficient, OR
- That our adjustment for risk is incorrect
The small-firm-effect
Companies with lower market capitalizations outperform companies with larger market capitalizations in the US, after accounting for risk
The book-to-market-effect
Companies with smaller BTM ratios were outperformed by companies with larger BTM ratios, after accounting for risk
Explain briefly event study methodology
- A way to test the impact of “news” on stock prices
- Basic idea: Estimate the expected return of a stock on a given day. The difference between observed return and expected return is the unexpected return that is attributable to the “news” → the “abnormal” return
What are the steps in “Event study”
- Determine event day
- Estimate the expected return (using market model)
- Estimate the abnormal returns
- Assuming that the “news” impacts the returns over more than one day we can sum abnormal returns to end up with a cumulative abnormal return
One way to test the market efficiency is to estimate the returns of company insiders (managers): They do possess material non-public information, what are the expected implications?
→ Under the strong-form EMH, their trades should be unprofitable, since private, non-public information is also contained in market prices
→ Under the semi-strong-form EMH, their trades should be profitable since the broad public is not aware of private information
Caminschi and Heaney (2013) did a study on gold “Fixings”, what was their findings and conclusion?
They found significantly elevated levels of trade volume and price volatility immediately following the fixing’s start, well before the conclusion of the fixing and the publication of its results, this implies:
→ Information from the fixing is leaking into markets prior to the fixing results being published
→ There exist economic returns for trading on this non-public information
→ The market for gold does not seem to be strong-form efficient (Same as security markets)
The most important risk for fixed income securities? How does it affect the bond price?
• Changing interest rates represent the most important risk for fixed income securities:
Higher interest rates → higher discount factor → lower price
Lower interest rates → lower discount factor → higher price
→ The price of a bond c.p. falls with rising interest rates and the relation between the price of a bond and the interest rate is convex
An investor considering a bond investment observes, and he neglects
Observes: - the par value, - the coupon rate of the bond, - the time to maturity, and - the current price of a bond Neglects: - the discount rate, which is equal to the promised rate of return over the remaining holding period of the bond
The yield to maturity (YTM)
Is the discount rate that makes the present value of a bond equal to its currently observed market price
The yield to maturity is the compounded rate of return until maturity (assuming reinvestment at that same rate)
Bond returns can come from two different sources:
− changes of the price of the bond
− coupon payments
What are the two names of non-par traded bonds?
− “Premium bonds” have price losses over time (they trade “above par”)
− “Discount bonds” have price increases over time (they trade “below par”)
Credit risk, short definition
- The risk that the issuer does not repay
Credit risk is composed of two main factors
- The probability of default (PD)
- The loss given default (LGD)
Rating agencies base their assessment of credit risk on a number of factors, among them:
− Coverage ratios: Ratio of earnings to costs (e.g., interest payments)
→ How many times annual earnings are required to repay annual interest?
− Leverage ratios: Ratio of debt to total assets (or debt to equity)
→ What is the relation of debt to total assets?
− Liquidity ratios: Ratio of current assets to current liability
→ How easily can a firm repay its current liabilities with its liquid assets?
− Profitability ratios: Ratio of profit to total assets (or equity)
→ Does the firm make a profit?
Transition matrices
The annual likelihood to change from one rating category to another is shown in so-called transi-tionmatrices
In terms of bond yields, it is important to distinguish between
− The promised yield, which is only realized when an issuer meets all obligations
− The expected yield, which takes into account default expectations
→ The promised yield is the maximum yield to maturity possible
Corporate bonds
Issued by companies and are subject to default and offer a default premium as compensation:
- The default premium is the promised yield of a corporate bond less the yield on an otherwise identical risk-free government bond
A Credit Default Swap (CDS)
Is an insurance against default on a bond. The annual premium paid for a CDS of a certain company is approximately equal to the yield spread between a risky corporate bond and an AAA rated bond.
But CDS do not only serve an insurance purpose, they are also means for speculation → CDS are heavily criticized
- Oftentimes, CDS contracts are more liquid than the underlying bonds
- They offer an insightful perspective on financial health of a company
yield curve
The relationship between maturity and yield of a bond is called yield curve
STRIP (Separate Trading of Registered Interested and Principal of Securities)
Institutional investors often “strip” a bond by reselling cash flows repaid at different points in time
− Each single cash flow represents a zero coupon bond, the sum of the parts is the value of the bond
− We can infer the yield curvefrom each STRIP
What if the sum of the parts in STRIP would be worth more (or less) than the entire bond?
→ Arbitrage: Investors would replicate the bond using STRIPs until the arbitrage opportunity vanishes
Risk-averse bond investors require what?
A premium to invest in bonds with longer maturity in order to bear risk that interest rates deviated from expectations
Theories of the term structure: The expectation hypothesis
Forward rates equal market expectations
→ No liquidity premium exists
The expected return of a long-term investment equals the expected return of repeated short-term investments
Yield to maturity is solely determined by current and expected future one-period interest rates
→ An upward sloping yield curve indicates that investors expect interest rates to increase in the future
Theories of the term structure: The liquidity preference hypothesis
Investors prefer liquid (i.e., short-term) investments over long-term investments. Issuers (e.g., companies) prefer long-term securities.
Investors require a premium when investing long-term
The expected return of a long-term investment is larger than the expected return of repeated short-term investments
The term structure depends on?
- Expected future interest rates, which in turn depend on:
- > Expected real interest rates
- > Expected inflation
- Liquidity premium
Interest rate risk, four graph characteristics:
− Negative slope:
Bond prices and yields are inversely related
− Convex:
An increase in the yield results in a smaller price
change than a similar reduction in yield
− Maturity:
Long-term bond prices are more yield sensitive
− Coupon:
Low-coupon bonds are more yield sensitive than prices of high-coupon bonds
Rules for the duration
- The duration of a zero-bond always equals the bond’s maturity
- The duration is lower the higher the coupon rate is.
- The duration (usually) increases with time to maturity.
- The duration of a bond increases with reduced yield to maturity.
- The duration of a perpetuity is (1+y/y)
Duration: Limitations, how do we solve it?
- The duration is only an approximation for the influence of interest rate changes on bond price changes
- Duration as an approximation works better for smaller yield changes
- Solution: We can enhance the ability to proxy for real bond price changes by adding a convexity term
Derivative
A derivative is a security whose price is determined (“derived”) primarily from the price of another security
A derivative is also called a “contingent claim”
Derivatives exist in a wide array of types and forms, among others: Conditional derivatives: - Options Unconditional derivatives: - Futures/ Forwards - Swaps
Options offer two interesting features
- Options offer leverage
- Options offer insurance
→ Combining option investments with investments into bonds and stocks offers interesting insights
Protective Puts
- If you want to own a stock, but are afraid of the downside risk, you can buy a stock and buy a put option
- This position is called a Protective Put since we use the put to protect us from the downside risk
- The Put serves as an insurance and the premium paid for the Put is the cost of insurance
Covered Calls
- Assume you want to buy a stock, but you already know that you will sell it if the stock exceeds a certain price → Write a call when buying the stock and collect the premium as additional income
- This position is called a Covered Call since the potential obligation to deliver the stock is covered by the stock already owned
- Writing a call without owning a stock is called a naked short position
Straddles
• Options also allow to speculate on up and down movements of the underlying at the same time
• If an investor believes that the underlying’s price will change, but does not know the direction, he can:
− Buy a call and
− Buy a put with the same exercise price.
This position is called a long straddle
Spreads
- Spreads allow the investor to participate in stock price movements, but only within a pre-defined price range
- Investors can thus reduce risk exposure to extreme portfolio values
- Spreads are set up by buying and selling a call with the same expiration date, but different exercise prices
- We can differentiate between bullish spreads (Exercise price of Long Call Exercise price of Short Put)
Put-Call-Parity
- Combinations of securities that yield the same payoff at expiration and have the same risk, both must have the same price today (=same initial investment)
- It is based on the no-arbitrage assumption
- This special relation is known as the Put-Call-Parity
- It follows that the value of a Put and the value of Call are not independent from each other
Callable bonds
− A callable bond is a bond that can be redeemed by the firm
− The issuing firm has the option to buy the bond back at a certain price (call long)
− As bond investor, you own the bond, but are short a call on the bond
→ Investors receive a higher coupon as compensation for the short position
Convertible bonds
− A convertible bond is a bond that can be exchange into shares of the same company by the holder of the bond
− By issuing the bond, the firm writesa call option to issue shares in exchange for the bond
− As bond investor, you own the bond, and you are long a call on the shares
→ Investors receive a lower couponas a compensation for the calloption on the shares
The intrinsic value of an option
Is the payoff of an option assuming the option is exercised immediately at the current price of the underlying, where it will be one of three stages:
- In-the-money
- At-the-money
- Out-of-the-money
The time value of an option
Is the difference between the current market price (𝐶 and 𝑃) and the intrinsic value of an option, the price is diven by, e.g:
=> Volatility, higher volatility means it is more likely to end up in the money
=> Time, the more time remaining until expiration, the higher the likelihood that the option will be exercised at expiration
Is the value of an out of the money option always negative?
Even if an option is currently out of the money
- It can still sell at a positive price since it has the potential to expire in the money
- The more time remaining until expiration, the higher the likelihood that the option will be exercised at expiration
When is time-value at its largest?
When the stock price currently trades around the exercise price (the option is ATM), time-value is largest since small changes in the stock price have a high impact on the payoff of the option
Should options be exercised before expiration
→ Call option: Because of the time value of money, it costs us more to buy the underlying today than to buy it at expiration! Never exercise CALL options on non-dividend paying stocks prior to expiration
→ Put options: The right to exercise prior to option expiration must have value, which is shown by the following example:
- A firm is bankrupt and the stock drops to zero. As a holder of the put option, you would want to exercise now. Because the stock cannot fall anymore, you would get the maximum payout possible today and start earning return on that money.
The Hedge ratio can be interpreted as?
- The range of possible call prices scaled by the range of possible stock prices
- The so-called Hedge ratio indicates the relation between shares and calls in the hedge portfolio
The idea behind Black and Scholes
The idea is that the price of the underlying (and therefore the price of the option) always change, thus the length of the intermediate steps in the price path become infinitesimally small (short),
What are the two main assumptions behind Black and Scholes
− The risk free interest rate is constant over the life of the option
− The volatility of the underlying is constant over the life of the option
Forward contract, what are the two positions
Agreement between two parties to exchange an asset in the future for a price fixed today. Gains and losses from Forwards are settled at DELIVERY date
−
Long position: Commits to purchase the underlying and to collect the underlying on delivery date
−
Short position: Commits to sell the underlying and to deliver the underlying on delivery date
Futures
Are standardized forward contracts that are traded on regulated exchanges. Gains and losses from a Future are settled DAILY.
- Standardization refers to Contract size, Quality, Contract delivery dates and location, Margins, et cetera
Futures main advantage/disadvantage
- Main disadvantage of standardization: Flexibility in formulation of contract is reduced → Often not perfectly usable for hedging
- Main advantage of standardization: Higher liquidity in the market since parties only have to agree on the price
The difference between options and futures
Options are conditional derivatives
→ The payoff is asymmetric since it depends (is conditional) on whether the long party exercises the option or not
Futures are unconditional derivatives
→ The payoff is symmetric since it is independent of (unconditional from) the action undertaken by both parties
→ Instead of four possible positions in option contracts, only two exist in futures contracts
Clearinghouses
Rather than having long and short traders holding contracts with each other (A), futures trading takes place via so-called clearinghouses (B)
Their role is to be the
- Seller of the contract to the long position and
- The buyer of the contract to the short position.
→ Clearinghouse has a net position of zero.
“Open interest” in futures
The “Open interest” is the number of contracts outstanding
Example:
- If a Future starts trading, open interest is zero.
- If a trader enters into one long contract, open interest increases to one.
→ Usually, traders close out their position prior to delivery and receive the profit in cash in order to prevent physical delivery of the underlying (only 1-3% delivered)
Forward vs. future pricing
The spot-futures parity theorem assumes that any payments are made on delivery, which is not applicable for futures pricing due to marking to market
→ Parity should only hold for Forwards
This will result in differing prices between Forwards and Futures if marking to market gives either the short or the long position a systematic advantage
→ A forward trader with a long position benefits from rising prices when interest rates are high
→ A forward trader with a short position benefits from falling prices when interest rates are high
Expectation Hypothesis
Simplest theory: The expected profit to both long and short positions is zero
Assumes that all market participants are risk-neutral: Risk premia are zero.
Normal backwardation
Majority of market participants are natural hedgers that want to short commodities. They are willing to pay long speculators a premium to take the long position of the contract.
Over time, futures prices rise until delivery, where future=price
Contango
Natural hedgers can also be long hedgers (e.g., grain processors).
Short hedgers are outnumbered by long-hedgers.
The Michelle Markup (David Yermack 2011)
- Michelle Obama increases shareholder value by 5 billion and increase of 1.7% one week after major event, and half of it during minor events.
- She is giving more value than sponsored people, i.e. they are ineffective since M. Obama creates more value, might be since she is considered credible and objective in her choices (J-Crew example, 8% next day and 25% by end of the week)
