### Create a StudySoup account

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

Already have a StudySoup account? Login here

# InvestmentAnalysisandPortfolioManagement FINC852

UD

GPA 3.82

### View Full Document

## 61

## 0

## Popular in Course

## Popular in Finance

This 32 page Class Notes was uploaded by Norberto Hessel on Saturday September 19, 2015. The Class Notes belongs to FINC852 at University of Delaware taught by Staff in Fall. Since its upload, it has received 61 views. For similar materials see /class/207110/finc852-university-of-delaware in Finance at University of Delaware.

## Reviews for InvestmentAnalysisandPortfolioManagement

### 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: 09/19/15

Chapters 58 Portfolio Theory Section 2 Outline 6 Chapter 5 Interest Rates and Risk Premiums See notes from first lecture 6 Chapter 6Risk and Risk Aversion Utility theory Indifference Curves 9 Chapter 7 Capital Allocation gtgt The opportunity set Capital Allocation Line The Optimal choice 9 Chapter 8Optimal Risky Portfolios Diversi cation gtgt The Opportunity Set Efficient Frontier 9 Two risky assets 0 Many risky assets The Optimal choice Holding period returns e The holding period return measures the return earned over a period of time Time period is not de ned 0 HPR capital gain yield dividend yield this assumes dividend is paid at end of period if received earlier this equation misses dividend reinvestments e If dividend yield 0 it is often calculated as HPR 131130 1 Multiple period returns EXDS monthly prices for 12 months Date Sep99 Oct99 Nov99 Dec99 Jan00 Feb00 Mar00 Apr00 May00 Jun00 Jul00 Aug00 e The arithmetic average return is Close 180156 215 269531 444062 574375 71 1875 7025 442188 352812 460625 444375 684375 Return 0 1 9341 0253633 0647536 0293457 0239391 0 01 31 7 0 37055 0 2021 2 0305582 0 03528 0540084 Cumulative 1 1 1 9341 1 496098 2 464875 3 1 88209 3 951 437 3 899398 2 454473 1 958369 2 55681 2 2 46661 2 3 798791 10 Jul99 Aug99 Oct99 Dec99 Jan00 Mar00 May Jun00 Aug00 Oct00 00 r sum ofretums N 016831 so if I invest 1 at this rate per month after 11 months I should have r116831 55352 5 but is this correct Arithmetic average ignores compounding More multiple period returns Geometric average does not ignore compounding rg 1Iqlr2lrnl 1 Date Sep 99 Oct 99 Nov 99 Dec 99 Jan 00 Feb 00 Mar 00 Apr 00 May 00 Jun 00 Jul 00 Aug 00 ltgt In the case of EXDS ltgt rg 37987911111 1290 Close 1 801 56 215 269531 444062 574375 711875 7025 442188 352812 460625 444375 684375 Retu rn 0 1 9341 0253633 0647536 0293457 0239391 0 01 31 7 0 37055 020212 0305582 0 03528 0540084 0 1 68361 Cumulative 1 1 9341 1 496098 2464875 3 1 88209 3 951 437 3 899398 2454473 1 958369 2 55681 2 246661 2 3798791 10 1 1 9341 1 253633 1 647536 1293457 1239391 0986831 0629449 0797878 1305582 0964722 1540084 3798791 ltgt the future value of 1 invested at 129 for 11 months is 112911 3798791 Chapter 6 Risk and Risk Aversion e Suppose an Investor has 100000 to invest and she has the following investment choices A A riskfree asset that pays a guaranteed 3 B A risky asset which pays either double or half with equal probability What is the expected endof period wealth from A What is the expected endof period wealth from B What is the expected return from B Simple Example o How should the investor decide which investment to take First calculate the riskpremium or excess return ER Rf 2y03 22 Next calculate a measure of risk One possible measure is standard deviation or variance 0391 252 5 252 562575 0 Is the riskpremium enough to compensate the investor for the risk Portfolio Returns 1 Historical Data gt If we expect that the past represents a good predictor for the future 2 Scenario Analysis gt Project out a number of possibilities gt Weight prospective returns by probabilities 3 Using riskpremium andor ad hoc expected return models Chapter 7 after midterm Historical Data e Suppose we owned ENE and EXDS over one year Date EXDS ENE Sep99 180156 407156 Oct99 215 396001 Nov99 26 9531 37 8663 Dec99 444062 441463 Jan00 57 4375 67 5252 Feb00 711875 68 5262 Mar00 7025 746313 Apr00 442188 69 4606 May00 352812 727678 Jun00 46 0625 644051 Jul00 444375 736415 Aug00 684375 84 7502 e EXDS return 684375180156 1 37987 e ENE return 847502407156 1 10815 4 Return on portfolio depends on the weight invested in each asset Q rp W W r exdsrexds ene ene if 50 each r 537987 510815 24401 or 24401 Portfolio returns O In general I l GZmn i1 where iwi 1 i1 9 The portfolio return is a weighted average of the individual asset returns Scenario analysis 0 Three basic steps Consider the scenarios that may occur Attach probabilities and returns to each scenario calculate the Er scenario pS Rule 1 Er 2 mm sl ACADNA scenario ps wNA HPR 02 005 03 025 04 005 01 01 HPR psHPR 0 2 0 05 0 01 03 0 25 0 075 04 005 002 01 01 0 01 sum 0075 Variance and standard deviation ltgt Historical data for EXDS and ENE ltgt Use a spreadsheet lt3gt Our exante measure is Rule 2 OZZHZpsI S Erz and 02 s1 Da te Sep 99 Oct 99 Nov 99 Dec 99 Jan 00 Feb 00 Mar 00 Apr 00 May 00 Jun 00 Jul 00 Aug 00 mean var std 1 2 3 4 scenario ps 02 03 04 01 HPRA EXDS 01 9341 0253633 0647536 0293457 0239391 001 31 7 037055 02021 2 0305582 003528 0540084 0 1 68361 0091 732 0302872 005 025 005 01 std ENE 00274 004378 0 1 65847 0529578 001 4824 0089091 006928 004761 3 0 1 1 492 01 4341 1 0 1 50848 008053 0031 1 04 0176364 psHPR pr Er quot2 001 0003125 0075 0009188 002 000025 001 0003063 0075 0015625 0125 Variance and standard deviation 0 Our exante measure is 02 zipsm EQDZ and 039ng scenario ps HPRA psHPR pr Erquot2 1 02 005 001 0003125 2 03 025 0075 0009188 3 04 005 002 000025 4 01 01 001 0003063 sum 0075 0015625 std 0125 Covariance and Correlation e EXpost the covariance is measured as 71 2 PM rjrk l rk 11 0 ch n 9 EXante the covariance is measured as 0 1216 2 219103 Erjrki Erk Q What does covariance measure 9 Correlation is a standardized covariance 039 j y k pjk 039j039k Portfolio variance Rule 5 e For 2 assets portfolio variance is 2 2 2 2 0p w10391 w20392 2w1w203912 O In a 3asset portfolio we must consider the covariance between each asset pair 12 13 and 23 2 2 2 2 2 2 0p w10391 w20392 W303 2w1w203912 2w1w303913 2w2w303923 Q In a nasset portfolio 9 or restated as N N 2 o P Z Zwiwjo tj i1 i1 More portfolio variance a In general the portfolio variance has N2 terms N variance terms N2 N covariance terms 0 For an equally weighted portfolio 2 11m 0P average covarlance N gt00 0 In a welldiversified portfolio we only bear covariance risk 0 This is risk is most often referred to as systematic risk or market risk Conceptual Portfolio Variance NXN terms mostly covariances Var Cov Cov COV Cov Cov Cov Var Cov COV Cov Cov Cov Cov Var COV Cov Cov Cov Cov Cov Var Cov Cov Cov Cov Cov COV Var Cov Cov Cov Cov Cov COV Cov Cov Var Should we consider anything besides variance ltgt If returns are normally distributed we need not consider higher moments skewness kurtosis if not normal we always prefer distributions skewed to the right ltgt Other risk measures often considered 1 Tracking error recall ETFs and mutual funds 2 Probability of shortfall risk of portfolio falling below a certain clientspecific value 3 Liquidity risk gtgt can t buy sell when we want to ltgt Generally we will only be interested in variance standard deviation and tracking error when appropriate Chapter 7 Utility Q Utili is an economic concept used to describe a person s preferences 9 Quadratic Utility U 1202 ER A 01 O A de nes the risk preferences AgtO implies risk aversion We generally assume that individuals are risk averse investors prefer higher expected return and lower risk Indifference Curves remember ECON Q We can use utility to de ne the combinations of risk and return investment choices that would provide the investor with the same utility level Example What combinations of risk and return would provide a utility level of 05 for an investor with A2 ER 5 Utility URER5A52 005 000 U 05 0 05 010 7 05 015 7 05 020 05 Indifference Curves O A graphical representation Q For our example With U05 and A2 03 025 02 015 01 005 0 l l t 0 01 02 03 04 05 Q What about A4 What about U10 Capital Allocation 0 Assume there are two securities 1 One r1sky portfoho P ERP15 0P 2 22 ii One riskfree asset F RF7 e What proportion of our investment do we allocate to P weight w and What proportion to F lw a Rule 2 only true in the case where one asset 00 2 2 2 0Cw op The Capital Allocation Line e Rules 1 and 2 give the Capital Allocation Line CAL MC 2 Rf a P The CAL defines all of the possible combinations of the risky and riskfree security for different weights The RewardtoVariability ratio is the premium excess return per unit of portfolio risk 15 07 In our example ERc 007 TJUC The Capital Allocation Line CAL e The CAL is a graphical representation of the possible riskreturn combinations associated with different weights w ER CAL Q 15 Slope Riewardtovariability ratio Rf7 K Q 22 0 6 What about margin positions 9 What if you cannot borrow at the riskfree rate Speci c Investment Objectives ltgt What portfolio weights would we choose to create a portfolio with a standard deviation of 10 1 w22 gt w 4545 What is the expected return on this portfolio ER 07 45451507 1063 Q What portfolio weights wou d we choose to create a portfolio with an expected return of 20 2 07 w1507 gt w 1625 What is the risk of this portfolio cc 162522 03575 Optimal Capital Allocation 9 An Investor confronted with the Capital Allocation Line of investment opportunities must choose an optimal w How c Find the weight W that maximizes utility given all possible portfolios on the CAL ie maximize utility subject to rules 1 and 2 Example If UR 02 ER y2A02 Then w 2 AO39P Optimal Capital Allocation 0 How do we graphically represent the optimal capital allocation decision Utility is maximized at the point of tangency between the CAL and the investor s indifference curves ER CAL Std DeV Optimal Capital Allocation 0 What happens to wquotlt when A increases Negative relation between A and w 62 increases Negative relation between 62 and w ERP RF increases Positive relation between ERP RF and w The Risky Portfolio 13gt Why do investors hold portfolios 13gt Risk re ects different sources of uncertainty Systematic Risk general economic conditions Unsysiemaiic Risk activities speci c to the rm a By investing in a range of securities the portfolio can be insulated from exposure to firmspecific risk Q Can portfolio risk be diversi ed away completely Q Can we reduce the risk of a portfolio more effectively Two Risky Assets 0 Consider the following two assets A ERA 8 0A 27 B ERB 16 03 2 20 o How do we describe the expected return and risk of a portfolio in terms of the returns on the individual securities that make up the portfolio Rule 1 ERP wERA l wERB Rule 2 0 wzof1 l w2039 2wl wC0vRARB With perfectly negative correlation 9 p1 W ERp GP 05 200 335 00 160 200 05 120 65 0741 101 00 10 80 70 15 40 205 ER 2000 1600 W 1200 W 4 800 W 400 W 000 1 1 1 000 1000 2000 3000 4000 Std Dev 6 Note If p1 we can create a perfect hedge Q What must be the riskfree rate in this economy

### 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

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

#### "When you're taking detailed notes and trying to help everyone else out in the class, it really helps you learn and understand the material...plus I made $280 on my first study guide!"

#### "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.