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FBE441_02_Quantitative_Review

# FBE441_02_Quantitative_Review - FBE 441 Investments Prof...

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FBE 441 Investments Prof. David Solomon Lecture 2: Quantitative Review Quantitative Review: Returns on assets and portfolios Stats: means, variances, covariances, distributions Regressions Readings: BKM chapter 5 (5.4,5.5 and 5.6)

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2 - How to measure returns? for assets & portfolios - How do returns behave? random variables, means, variances - How do returns move together? covariances and correlations - Probability Distributions Part A - Outline: - How do returns move together? . Regressions . Testing hypotheses Part B - Outline:
3 How To Measure Asset Returns? Holding period return on an asset : Return = capital gain + dividend yield (or other income) Sometimes, you also need to include transaction costs A negative return is a loss Conventions for quoting returns 1% return = 0.01 usually annual returns, but we may come across semi- annual, quarterly, monthly, or daily returns r i , t = ( P i , t - P i , t -1 ) + D i , t P i , t -1

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4 (Side Note): Do not sum returns over multiple periods! Arithmetic Average Return r a = (r 1 + r 2 + r 3 + ... r n ) / n r a = (.10 + .25 - .20 + .25) / 4 = .10 or 10% Geometric Average Return ( use this !) r g = {[(1+r 1 ) (1+r 2 ) .... (1+r n )]} 1/n - 1 r g = {[(1.1) (1.25) (.8) (1.25)]} 1/4 - 1 = (1.375) 1/4 -1 = .0829 = 8.29% Year1 Year2 Year3 Year4 Ret 0.10 0.25 -0.20 0.25 How To Measure Asset Returns?
5 How To Measure Portfolio Returns? Measuring return of a portfolio : The return on a portfolio is a value-weighted average of the returns on the component assets N N r w r w r w + + + = = = ... r r 2 2 1 1 N 1 i i i p ϖ where ϖ i , is each asset’s portfolio weight r i , is each asset’s return

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6 An asset’s portfolio weight , ϖ i , is the percentage of the portfolio’s total value invested in that particular asset. The weight held in each stock, is: Portfolio weights can be positive (a “long” position) or negative (a “short” position) Portfolio weights should always add to one ( ϖ 1 +..+ ϖ N =1) - If you buy a stock … - If you short-sell (borrow) a stock … - If you deposit money (buy a risk-free security) … - If you borrow money (borrowing risk-free) …
7 Investing in Equity : go long (+) go short (-) buy: short-sell: buy on margin:

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8 Example : . You have \$100,000 to invest . ABC shares: ABC is trading at \$10/share In 1-year: ABC pays \$1 in dividends, trades at \$11/share . Risk-free deposit r f = 5% per year -> r ABC = ? -> r portfolio = ?
9 Portfolio A : buy 10,000 shares of ABC w ABC = w f = Portfolio B : buy 5,000 shares of ABC, deposit at 5% w ABC = w f = Portfolio C : buy 20,000 shares of ABC on margin and borrow at 6% (assume no margin call) w ABC = w f = Portfolio D : sell-short 10,000 shares of ABC, deposit at 5% w ABC = w f = Portfolio E : sell-short 5,000 shares of ABC, deposit at 5% w ABC = w f =

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10 What are the realized returns ? – r A = – r B = – r C = – r D = – r E =
11 What if ABC is worth \$8/share in 1-year? – r A = – r B = – r C = – r D = – r E = What if ABC is worth \$8/share in 1-year and the transaction costs are 50bps (round-trip)?

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