CAIA 48 – 55 EXAM QUESTIONS WITH COMPLETE SOLUTIONS

Multi-factor models express systematic risk using multiple factors and are extremely popular throughout traditional and alternative investing. The reason is simple: multi-factor models tend to explain systematic returns much better than do single-factor models. general ex ante form of a multi-factor asset pricing model general ex poste form of a multi-factor asset pricing model ex poste vs ex ante ex ante models describe expected returns while ex post models describe realized returns. A factor A factor represents a unique source of return and a unique premium in financial markets such that the observed return cannot be fully explained by other factors. In other words, return factors are not supposed to be highly correlated with each other. Multi-factor models of asset pricing express systematic risk using multiple factors and are extremely popular throughout traditional and alternative investing. The reason is simple: multi-factor models tend to explain systematic returns much better than do single-factor models. By doing so, multi-factor models are generally believed to produce better estimates of idiosyncratic returns. Macroeconomic factors macroeconomic factors related to asset returns throughout the entire economy and across asset classes, and include productivity, inflation, credit, economic growth, and liquidity Fundamental, style, investment, or dynamic factors these drive equity returns within asset classes and include well known style factors such as value, size, momentum, quality, and low volatility. These factors are linked to fundamental firm attributes that have been empirically identified as being important drivers of different investment returns across various firms, industries, and sectors. These factors are used in smart beta and alternative beta approaches. Statistical factors distinguished by having been identified purely on empirical characteristics rather than style or economic characteristics. For example, principal component analysis of security returns through time may find that much of the return differences between assets can be explained by perhaps three to five components. The economic identity of these factors and economic cause of the relation between the factor and the asset returns is often not known a tradable asset position that can be readily established and liquidated in the financial market, such as a stock position, a bond position, or a portfolio of liquid positions. Alternatively, the factors may represent non-tradable variables, such as inflation or economic productivity. Fama-French model links the returns of assets to three factors: (1) the market portfolio; (2) a factor representing a value versus growth effect; and (3) a factor representing a small-cap versus large-cap effect.1 ex ante form of the Fama-French model: where Rs is the return to a diversified portfolio consisting of small-capitalization stocks, Rb is the return to a diversified portfolio consisting of big-capitalization stocks, β1i is the responsiveness of asset i to the spread (Rs − Rb), Rh is the return to a diversified portfolio consisting of high book-to-market ratio (value) stocks, Rl is the return to a diversified portfolio consisting of low book-to-market ratio (growth) stocks, and β2i; is the responsiveness of asset i to the spread (Rh − Rl). Fama-French-Carhart model adds a fourth factor to the Fama-French model: momentum. Fama-French-Carhart model ex ante where Rw is the return to a diversified portfolio consisting of winning stocks, in the sense that they have better performance over a previous period; Rd is the return to a diversified portfolio consisting of declining stocks, in the sense that they have worse performance over a previous period; and β3i is the responsiveness of asset i to the spread (Rw − Rd). The Fama-French five-factor model adds two factors to the Fama-French three-factor model: robust minus weak, and conservative minus aggressive. Robust minus weak factor the average return on... robust operating profitability portfolios minus the average return on... weak operating profitability portfolios. Conservative minus aggressive the average return on... conservative investment portfolios minus the average return on... aggressive investment portfolios A momentum crash occurs when those assets with recent overperformance (i.e., those assets with momentum) experience extremely poor performance relative to other assets (Asness et al. 2010). Adaptive Markets Hypothesis (AMH) an approach to understanding how markets evolve, how opportunities occur, and how market players succeed or fail based on principles of evolutionary biology...."Prices reflect as much information as dictated by the combination of environmental conditions and the number and nature of "species" in the economy, or ... ecology. Species are defined as distinct groups of market participants: e.g., pension funds, retail investors, hedge funds..." Time-Varying Risk Premiums The tradeoff between risk and return is not stable over time (risk premiums vary over time). In addition, changes in risk premiums could be predicted based on technical and fundamental variables. Market Efficiency is a Relative Concept. Market efficiency should be measured and discussed in relative terms as opposed to absolute terms. Market efficiency is a continuum; it is not simply efficient or inefficient, and a market displays varying degrees of efficiency at different points in time and for different market participants. Adaptation for Success and Survival It is necessary to use adaptable investment approaches to handle changes in the market environment. Opportunities are not always found in the same place; therefore, trading strategies must be altered as the economic environment evolves. The Inevitable Degradation of alpha With time, what was once alpha becomes, due to innovation and competition, beta. Persistent alpha opportunities are not possible; however, fleeting alpha opportunities may be possible. Time-varying volatility the characteristic of a return series in which the asset's returns experience varying levels of true (as opposed to realized) return variation.... which simply means that the asset's volatility is not constant The Heston model allows the volatility of the asset to change randomly through time in a continuous process that reverts to a long-term average The Bates model treats volatility as a stochastic process much like the Heston model except that it includes a jump process for the underlying asset's price that permits price jumps at random time intervals and with random magnitude. The modeling process comes down to a decision of whether random changes in equity prices through time are driven purely by a volatility process that is itself random or whether the price changes are also the result of random price shocks.