CAIA TOPIC 2 QUESTIONS WITH 100% CORRECT ANSWERS 2023.

Normal Distribution ○ Normal curve is symmetrical ○ 2 halves are identical ○ Doesn't hit zero but gets close ○ Mean = mu ○ Width = standard deviation = sigma ○ Values often thought as distance from the mean in standard deviations § Z value...how many standard deviations away from the mean LO 2.6.6.1: Demonstrate knowledge of the concept of informational market efficiency. The three forms of market efficiency include weak form (security prices fully reflect all available security data on past prices and volumes), semistrong form (security prices fully reflect all publicly available information) and strong form (security prices fully reflect all publicly and privately available information). Six factors that result in improved informational market efficiency are: (1) larger asset values, (2) higher frequency of trades, (3) little or no trading frictions, (4) low levels of regulatory constraints, (5) easier access to quality information, and (6) lower levels of uncertainty about asset valuation. LO 2.6.6.2: Demonstrate knowledge of single-factor asset pricing models and ex ante pricing. The ex ante form of the capital asset pricing model (CAPM) is an equilibrium model that derives the expected return on a stock given the expected return on the market portfolio, the stock's beta coefficient, and the risk-free rate: E(Ri) = Rf + βi[E(Rm) - Rf]. The ex post CAPM focuses on realized returns: Ri,t - Rf = βi(Rm,t - Rf ) + εi,t. The CAPM implies that the expected return on any asset is solely determined by its systematic risk (beta) and that no additional expected return will be earned by bearing non-systematic or idiosyncratic risk. The CAPM also implies that all investors should use a two-fund strategy of investing a portion in the risk-free fund and the remainder in a well-diversified risky fund. Asset pricing models can be used to separate risks and returns into diversifiable (idiosyncratic) and non-diversifiable (systematic) components and to quantify the compensation expected to be received for risk. LO 2.6.6.3: Demonstrate knowledge of multifactor and empirical asset pricing models. Multifactor asset pricing models describe the relationship between expected returns for an asset and its exposures to multiple risk factors: E(Ri) - Rf = βi,1[E(R1) - Rf ] + βi,2[E(R2) - Rf] + ...+ βi,K[E(RK) - Rf]. Theoretical models are based on assumptions and logic that presumably captures underlying behavior. In contrast, empirical models are based on historically observed behavior. The main weakness with empirically derived multifactor models is that the factors may have been identified from spurious correlations (correlations between factors that are purely coincidental). The steps to derive an empirical multifactor model are: Derive excess returns for the security (the dependent variable of the ex post regression). Identify a set of potential factors. Perform tests of significance to identify the important "priced" factors. Assuming the factors are tradable assets (i.e., rates of return can be observed), the intercept of the ex post multifactor model reflects the abnormal performance of the security. The Fama-French three-factor model is an empirical multifactor model which states that E(Ri) - Rf = β1(Rm - Rf) + β2 E(SMB) + β3 E(HML), where Rm - Rf is the excess return, SMB is the size factor equal to the difference in returns between small and big firms (Rs - Rb), and HML is the book-to-market factor equal to the difference in returns between high and low book-to-market firms (Rh - Rl). The Fama-French-Carhart four-factor model states that E(Ri) - Rf = β1(Rm - Rf) + β2 E(SMB) + β3E(HML) + β4 E(UMD), where UMD (or the momentum factor) equals the difference in returns between stocks that were up the most and those that were down the most during the prior year. Factors should be selected based on solid theoretical rationale or based on rigorous statistical testing. Three caveats are in order when deriving factors. First, we should not indiscriminately test a multitude of factors. Second, we should avoid identifying factors based on spurious correlation. Third, the CAPM does not work well for alternative assets, which could have large idiosyncratic risks that are not easily diversified away. LO 2.6.6.4: Demonstrate knowledge of arbitrage-free financial models. In the simplest forward pricing model: F(T) = S for all maturities, T Cost of carry is a measure of the financial difference between holding a position in the spot market and holding a position in the forward market. Any difference between the spot and forward price is due to the cost of carry, which causes the term structure of forward prices to have a slope or curve. The cost of carry relationship is as follows: F(T) = S + carrying costs Financial forwards include futures contracts on stock indices, U.S. Treasury bond futures, and Eurodollar CD futures. The pricing relationship for financial forwards is as follows: F(T) = S × e(r-d) × T A binomial tree model shows the possible values an option can take at each given time period, and reflects the uncertainty in outcome by modeling an upward and downward movement at each state. LO 2.6.6.5: Demonstrate knowledge of the term structure of forward contracts. There are four cost-of-carry model scenarios for financial securities. In a simple scenario with no interest costs and no dividends, there are no differences in forward prices and all forward prices equal the spot price. This results in a flat term structure of forwards. The interest rate equals the dividends rate, but both are positive. This also results in a flat term structure of forwards. The interest rate exceeds the dividend rate. When that happens, the no-arbitrage forward price must exceed the spot price and the term structure of forward prices is upward sloping. The dividend rate exceeds the interest rate, and the no-arbitrage forward price is lower than the spot price. The term structure of forward prices is downward sloping. LO 2.6.6.6: Demonstrate knowledge of option exposures. A covered call strategy combines being long the underlying security and being short a call option on the security. It has limited upside and limited downside. A protective put strategy combines being long the underlying security and being long a put option on the security, and has unlimited upside and limited downside. An option spread involves (1) either calls or puts and (2) both long and short positions on the underlying security. A bull spread combines a long position in a lower strike price option and a short position in a higher strike price option. A bear spread combines a long position in in a higher strike price option and a short position in a lower strike price option. Option combinations involve both calls and puts on the underlying security. An option straddle is a position in a call and a put (either both long or both short) on the same underlying security, same expiration date, and same strike price. An option strangle is a position in a call and a put (either both long or both short) on the same underlying security and expiration date, but with different strike prices. A risk reversal consists of a long out-of-the-money call combined with a short out-of-the-money put on the same asset and with the same expiration. A collar includes a long position in the underlying security, which is combined with a long put option and a short call option. Put-call parity is a no-arbitrage relationship between two sets of positions with identical payoffs: (1) a long underlying asset and (2) a long call, short put, and long risk-free bond. call + risk-free bond - put = underlying asset LO 2.6.6.7: Demonstrate knowledge of option pricing models. The basic option pricing model values an option on a portfolio that contains both long and short positions. The option gives the option holder the right to either purchase the entire portfolio or walk away and let the option expire. Po = PlN(d) − PsN(d − v) The Black-Scholes call option formula values a call option as a function of the price of the underlying security, the option strike price, the volatility of security returns, the option's time to expiration, and the risk-free rate: c = SN(d1) − e−rTKN(d2) A variation of this formula is the well-known Black-Scholes put option formula. The Black forward option pricing model replaces the underlying security in the Black-Scholes call option formula with the forward contract. c = e−rT[FN(d1) − KN(d2)] In the currency option pricing model, there are two risk-free interest rates that correspond to the two currencies that are exchanged. In other words, the model prices an option that gives the right to exchange S units of one currency with its associated r risk-free interest rate, for S units of another currency at r risk-free interest rate: option price = e−r TS∗N(d1) - e−rTSN(d2)