{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

429week04f07 - Week 4 Sep 17 Equity Risk Risk Defined...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Week 4: Sep 17 Equity Risk Risk Defined Random Walk Stat Review Portfolio Theory Portfolios Diversification (2 Securities) Examples/Progressive
Image of page 1

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

View Full Document Right Arrow Icon
Equity Risk Risk Defined What is Risk? Risk involves taking a chance => Probabilities Payouts must be represented by Expected Values. Risk is defined by variability in the possible future payouts For Bonds, we know exactly what the payouts will be. Is there risk? Variability is quantified by Variance 1. The existence of the possibility of large losses vs gains 2. The relative possibility of loss vs gains
Image of page 2
Equity Risk Random Walk To describe Returns with just the Expected Values and the Variance we need a model Normality of Returns We assume that returns follow a normal distribution Allows us to use standard tables to describe probability of returns Assume returns follow a random walk The next price will be any other price with a probability described by the Normal
Image of page 3

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

View Full Document Right Arrow Icon
Equity Risk Stock prices are NOT determined fundamentally, but by random motion => roots in Physics Empirical Evidence We do NOT find that stock prices follow a 0 10 20 30 40 50 60 3 2.5 2 1.5 1 0.5 0 0.5- 1- 1.5- 2- 2.5- 3- norm Value-Weighted
Image of page 4
Equity Risk Based on monthly data from CRSP (62- Present) Too much probability near the mean Fat tails (esp. on negative side) Positively Skewed
Image of page 5

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

View Full Document Right Arrow Icon
Equity Risk Stat Review Expected Value “Average” = what you would expect to receive from a game of chance (random outcomes) if you could play the game many times Notation: E(a) = Expected Value of a Properties Expected Value of Sum is Sum of Expected Values s x of x x x prob Value Expected ' # * ) ( = = ) ( ) ( ) ( y E x E y x E + = +
Image of page 6
Equity Risk Expectation of a Constant times x is the Constant times Expected Value of x For a linear combination of random variables We are interested in Expected Values because we know that if we have returns, we know the price ) ( * ) ( x E K Kx E = ) ( * ) ( * ) ( ) ( ) ( y E L x E K Ly E Kx E Ly Kx E + = + = + Return) ( 1 P(0) E(P(t)) Return 1 ) 0 ( ) ( E P t P + = + =
Image of page 7

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

View Full Document Right Arrow Icon
Equity Risk Variance Farther x’s are from E(x), larger the variance “The more outcomes there are that are very hi or very low, the more risk there is.” More likely x E(x), larger the variance Notation: Variance(x) = V(x) = σ x 2 Standard Deviation = Variance .5 = σ x s x' of # (x)) - (x Prob(x) * )) ( ( ) ( 2 2 = - = E x E x x V
Image of page 8
Equity Risk Properties Variance of constant times variable is Constant squared times Variance of the variable Variance of Sum of weighted variables is sum of weights squared times variances of each plus twice the covariance » Covariance is how much on variable moves with the other (direction and magnitude). » Notation: Covariance of x and y = Cov(x,y) ) ( )) ( ( )) ( ( )) ( ( ) ( 2 2 2 2 2 x V a x E x a x aE ax ax E ax ax V = - = - = - =
Image of page 9

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

View Full Document Right Arrow Icon
Equity Risk Note: Cov(x,y)= ρ xy σ x σ y » -1 ρ xy 1 is the correlation coefficient ) , ( 2 ) ( ) ( ) , ( 2 ) ( ) ( 2 2 ) ( ) ( ), ( )) ( ) ( ( ) ( 2 2 2 2 2 2 2 y x abCov y V b x V a by ax Cov by V ax V gh h g gh h g by ax V by E by h ax E ax g Let by E by ax E ax
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern