Chapter 7 - Models Of Asset Returns

Question 1

What is the distinction between systematic return and specific returns

Answer 1

-systematic return of a security i: is the element of the total return that arises due to an influence of the L factors that affect the returns on every security (b_i,1 I_1 + b_i,2 I_2 +… +b_i, L I_L) . Specific risk is unique to security i and is equal to a_i + b_i

Question 2

Why is it convenient for factors to be uncorrelated

Answer 2

• if there is no correlation it is easier to disentangle the influences of each security returns
• high correlation makes it difficult to do the above process since there will be insufficient independent variation to enable the model to isolate their separate influences
  Since we also use regression to determine which factors are significant, multicollinearity has an effect in making the coefficient estimates less efficient

Question 3

What are multifactor models of security returns?

Answer 3

They attempt to explain the observed historical return by an equation of the form:

R_i = a_i +b_(i,1)I_1 +b_(i, 2)I_2+…+b_(i,L)I_L

Where R_i is the return on security i
a_i and b_i are constants random parts that are unique to security i
I_1+…+I_L are the set of factors that cause a change in the return of the security
b_(i,1),…,b_(i,L) are sensitivities of the security i to the factors

Question 4

Specific risk

Answer 4

The risk that only affects an industry or a particular company - this can be diversified away

Question 5

Systematic risk

Answer 5

The risk that affects a large number of asset classes, this is sometimes called market risk - cannot be diversified away

Question 6

Macroeconomic Factor models

Answer 6

• use observable economic time series as factors
• factors are the main macroeconomic variables such as interest rates, inflation, economic growth and exchange rates, the yields on long-term government bonds, the yield margin on corporate bonds over government bonds
• are assumed to influence security prices and returns

Question 7

Fundamental Factor models

Answer 7

• are similar to macroeconomic models but instead of ( or in addition to ) macroeconomic variables, they use company-specific variables
• These include the level of gearing, the price-earnings ratio, the level of Research & Development spending
  the industry group to which the company belongs

Question 8

Statistical factor models

Answer 8

• do not rely on specifying the factors independently of the historical returns data instead a technique called principal components analysis can be used to determine a set of orthogonal indices that explain as much as possible of the observed variance

Question 9

when we look at single-factor models, how can we interpret alpha_i and beta_i

Answer 9

• alpha_i can be interpreted as the expected value of the component of security i’s return that is independent of the market’s performance and specific to that particular security
• beta_i quantifies the component of the security return that is directly related to movements in the market so that if beta_i = x, then security i ‘s return is expected to increase or decrease by x% when the market return increases or decreases by 1%

Question 10

Main uses of multifactor models and single-index models

Answer 10

1 - determination of investor’s efficient frontier, as part of the derivation of the investor’s optimal portfolio
2- Risk control- by enabling the investor to forecast the variability of portfolio returns both absolutely and relative to some benchmark
3- performance analysis - by comparing the actual performance to that predicted by the model based on the portfolio’s actual exposure to the relevant factors over the period considered
4- categorisation of investment styles - according to the extent of the exposure to particular factors

Question 11

what is the main limitation of the single-index model and multifactor models

Answer 11

• historical data reflects conditions that may not be replicated in the future
• models may produce good predictions for one particular time period but not the next