### Create a StudySoup account

#### Be part of our community, it's free to join!

Already have a StudySoup account? Login here

# Class Note for FINA 4320 with Professor Boulatov at UH

### View Full Document

## 20

## 0

## Popular in Course

## Popular in Department

This 38 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at University of Houston taught by a professor in Fall. Since its upload, it has received 20 views.

## Reviews for Class Note for FINA 4320 with Professor Boulatov at UH

### What is Karma?

#### Karma is the currency of StudySoup.

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 02/06/15

Class 9 Ef cient Diversi cation Firrn Speci c amp Market Risks Reduction of Speci c Risk Increasing of securities in portfolio A Risk Speci c Risk Market Risk n P TwoSecurity Portfolio Three Rules 1 Return rp W1r1 W2r2 W1 Proportion of funds in Security 1 W2 Proportion of funds in Security 2 2 Expected Return 3 Risk TwoSecurity Portfolio Exp Return rp W1r1 Wzr2 W1 Proportion of funds in Security 1 W2 Proportion of funds in Security 2 71 Expected return on Security 1 r Expected return on Security 2 n 2 Wi 1 i1 TwoSecurity Portfolio Risk 612 Variance of Security 1 622 Variance of Security 2 Covr1r2 Covariance of returns for Security 1 and Security 2 Covariance ef nition Covariance amp Correlation CQWH r2 5 91226162 9132 E Correiatien coefficient of returns 61 Standard devation et returns for Security 1 dz Standard devation et returns for Security 2 Correlation Coef cients Possible Values Range of values for p 1 2 4ogpg1o If p 10 the securities would be perfectly positively correlated If p 10 the securities would be perfectly negatively correlated MeanVariance Efficiency 0 Investors Prefer Asset A to Asset B if High Expected Returns LOW Risk Bene ts of Diversi cation Whenever assets are lessthanperfectly correlated diversi cation is bene cial This holds also for multiple assets more than 2 TWO Securities Example Bond GB 12 YB 26 Can we do Better Diversifv with Stock WB 075 0350 7p 20756 02510 7gt6 2 2 Up 07512 025252 120 Up V120 1096 lt 12 ThreeSecurity Portfolio ram 629 3 W1 2612 W226 32632 2W1W2 Covmrzl 2w1w3 Comm 2W2W3 COWFZT3 E W1 H Wzrz 1 Wars In General For an nSecurity Portfolio rp Weighted average of the rm securities spa Consider aii pairawise covariance measures TwoSecurity Portfolio Ema 5 N1 mm Wang 2 2 2 2 2 GP W12612 w22022 2W1W2 Covr1r21 2 E0 13 8 TWOSECURITY PORTFOLIOS WITH DIFFERENT CORRELATIONS Portfolio RiskReturn Two Securities Correlation Effects Relationship depends on correlation coef cient 10 p 10 The smaller the correlation the greater the risk reduction potential If p 10 no risk reduction is possible Minimum Variance Combination Sec i Er110 51 5A5 912 5 2 Sen 2 E02 5 E14 6 2 5 20 G g Covm 12 W1 L 5 6 I ZCovmrz W2 5 1 E W1 Minimum Variance Combination p 2 W 222152 1 152 22 22152 W16733 W2167333267 Minimum Variance Return and Risk With p 2 rp6733L103267L141131 G p 67332152 3267222 267333267215212 GIo 01711 2 1308 Minimum Variance Combination p 3 W 222152 1 152 22 22153 W16087 W2160873913 Minimum Variance Return and Risk With p 3 rp6087L103913L141157 60 60872152 3913222 260873913215312 GP 0102 2 1009 Extending Concepts to All Securities The optimal combinations result in lowest level of risk for a given return The optimal tradeoff is described as the efficient frontier These portfolios are dominant Example 3 Securities Three securities A B C have the following parameters and crosscorrelations What is the MVE frontier Rfrate 35 Cmrebutan Assets n B 392 t 1 I223 12139 CI 3 Ci 3 1 E3 E3 5 i 215 35 10 asset ljujfrju a A 5 llir39jiafg B 1113935s13 Est343 I 30 Three Securities MVE Frontier I I I I I I l 016 A B C AB Combinations D14 39 BID Comblnations 39 39 AC Combinations if lffquot u IF39 012 l F quot F u 39quot I quot39 39 r 39 quot 1 Iu 4quot i If 5 DDEE If sl anquot I I I quoth x 006 L Huh 004 uni 002 quot h Cl 39 a I H 0 02 I I Expected Return Three Securities MVE II I 1inimum Varianrze Fan lier 13918 014 012 U02 U DBL 01 015 12 Return Standard Deviation 025 The minimumvariance frontier of E r risky assets Efficient frontier Individual GlObal quot x assets EIEIEEIQEIEIEIEEIEI x variance portfono Minimum va ance frontier St Dev Extending to Include Riskless Xsset The optimal combination becomes linear A single combination of risky and riskless assets will dominate Dominating portfolio involves a single asset on MVE Frontier and a riskfree asset Twofund Separation Motivation See next slide ALTERNATIVE CALS CAL M uaaaamaaaaaaaaaaama fag II ll P immmmmlmmmw m 2 CAL Global g 3 minimum variance A 3 2 E 3 E E a 394 Is ll 2 E a E a I II I E I II II 394 In In F a 2 a a 3 2 E E I l I P PampF M AampF 6 Expected Return MVE With RiskFree Asset Fu linimum Varianrze Frontier 118 314 11112 01 Puljai39smpe F53 1 I 3 Mid Var l d i 002 UD 2 39 39 D 005 01 0515 02 025 03 Return Standard Deviaiio Dominant CAL With a RiskFree Investment F CALP dominates other lines it has the best riskreturn or the largest slope Slope ER Rf o ERP 39 Rf G P gt ERA 39 Rf GA Regardless of risk preferences combinations of P amp F dominate Therefore Depending on Investor s RA Choose a point on CAL Single Factor Model 1391 ERi 81F 6 Bi index of a securities particular return to the factor F some macro factor in this case F is unanticipated movement F is commonly related to security returns Assumption a broad market index like the SampP500 is the common factor Single Index Model ri rf05i6irm rfe l 1 Risk Prem Market Risk Prem or Index Risk Prem 0 i the stock s expected return if the market s excess return is zero rm rf 0 l3irm rf the component of return due to movements in the market index ei firm specific component not due to market movements Risk Premium Format Let R r 39 rf Risk premium Rm rm rf format R 0Li BiRm ei Estimating the Index Model Excess Returns i Security Characteristic Line Excess returns on market index Ri aiBiRmei Components of Risk Market or systematic risk risk related to the macro economic factor or market index Unsystematic or rm speci c risk risk not related to the macro factor or market index Total risk Systematic Unsystematic Measuring Components of Risk 2 2 2 2 Ci Bi 0m G 91 Where Giz total variance Biz sz systematic variance 02ei unsysternatic variance Examining Percentage of Variance Total Risk Systematic Risk Unsystematic Risk Systematic RiskTotal Risk p2 3120m202 p2 BiZ CSm2 BiZ sz C52ei p2 Advantages of the Single Index Model Reduces the number of inputs for diversi cation Easier for security analysts to specialize

### BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.

### You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over $600 per month. I LOVE StudySoup!"

#### "There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.