{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

(L13)APT(f)

# (L13)APT(f) - Lecture 13 The Arbitrage Pricing Theory(APT...

This preview shows pages 1–12. Sign up to view the full content.

Primbs/Investment Science 1 Lecture # 13 The Arbitrage Pricing Theory (APT) Reading: Luenberger Chapter 8, Sections 1 – 4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Primbs/Investment Science 2 Models, Data, and APT Models, Data, and APT Factor Models Relation to CAPM The Arbitrage Pricing Theory Means and Variances Well Diversified Portfolios
Primbs/Investment Science 3 The difficulty with mean-variance The mean-variance approach requires that you estimate the mean, variance, and covariance of all securities in your portfolio. This can be a huge number. For n stocks, we need n means, n variances, and n(n-1)/2 covariances. (for 1000 stocks, this is 501500 values to be estimated!) Clearly, we need an approach that requires less computation.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Primbs/Investment Science 4 Factor Models Rates of return are related to factors (which are random quantities). i i i i e f b a r + + = Consider the following model: random factor f constants b i is called the factor loading e i is a random error term with E[ e i ]=0.
Primbs/Investment Science 5 Factor Models i i i i e f b a r + + = Factors models correspond to using a linear regression to fit data. r i f x x x x x x x a i slope b i y-intercept ( factor loading ) e i x x x x x x x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Primbs/Investment Science 6 Multi-Factor Models i i i i i e f b f b a r + + + = 2 2 1 1 j j j j j e f b f b a r + + + = 2 2 1 1 We can also consider models where rates of returns are determined by more than a single factor. These are called multi-factor models. Assumption We will assume that the factors f 1 , f 2 , ... are uncorrelated random variables. Furthermore, we will assume that the error terms, e i , e j are uncorrelated with each other and with the factors. That is Cov(e i ,e j ) = 0 and Cov(e i ,f j ) = 0 .
Primbs/Investment Science 7 What are possible factors? External Factors: GDP, PPI, CPI, Unemployment, Interest Rates, etc... Extracted Factors: Market Portfolio, Industry Averages, etc... (One can also include firm specific factors such as size, price/book, etc. However, in the following APT theory only factors that apply to many firms will be relevant.)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Primbs/Investment Science 8 Models, Data, and APT Models, Data, and APT Factor Models Relation to CAPM The Arbitrage Pricing Theory Means and Variances Well Diversified Portfolios
Primbs/Investment Science 9 Calculation of Mean and Variance (Single Factor Model) The mean of a return is given by: f b a i i + = ] [ ] [ i i i i i e f b a E r E r + + = = ] [ ] [ i i i e E f E b a + + = Known: E(e i )=0 and cov(f,e i )=0 . ) ( i i i i e f b a r + + =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Primbs/Investment Science 10 Calculation of Mean and Variance (Single Factor Model) Known: E(e i )=0 and cov(f,e i )=0 . The variance is given by: ] )) ( ) [(( ] ) [( 2 2 2 f b a e f b a E r r E i i i i i i i + - + + = - = σ ] ) ) ( [( 2 i i e f f b E + - = ] ) ( 2 ) ( [ 2 2 2 i i i i e e f f b f f b E + - + - = ) var( ) , cov( 2 ) var( 2 i i i i e e f b f b + + = ) var( ) var( 2 i i e f b + = 2 2 2 i e f i b σ σ + = ) ( i i i i e f b a r + + =
Primbs/Investment Science 11 Calculation of Mean and Variance (Single Factor Model) Known: E(e i )=0 and cov(f,e i )=0 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 40

(L13)APT(f) - Lecture 13 The Arbitrage Pricing Theory(APT...

This preview shows document pages 1 - 12. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online