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Given a portfolio of two assets ER s and ER s if theBond Pricing Portfolio Selection Theory AABBexpected return is the weighted average of individual asset returns correlation coefficient is p what is the minimum portfolio ABbut expected risk is not the weighted average variance that can be achieved For 2 assetsFor namount of assetsApplication of the APT Minimum Portfolio Variance ExampleBond Pricing Example Covariance measures comovement of returnshigher covariance indicates greater comovementpositive moves in same direction while negative moves in oppositedirectionThree and FourFactor ModelsModels developed that includes the risk factors in microeconomic Bond prices and market interest rates have an inverse relationshipterms using the characteristics of underlying securities 3factor andwhen interest rates get high value of bond is low Correlation Coefficient formulaIn general the meanvariance opportunities of N risky assets can including a risk factor that accounts for tendency for firms withwhen interest rates are low value of bond approaches sum ofbe found by solving either of the following two mathematical positive past return to produce positive future return 4factor cash flowsprogramming problems The first defines the minimum variance Where 1p1 opportunity set and the second defines the efficient set Yieldtomaturity interest rate that makes the present value of the Market EfficiencyThe optimal lies at the point of tangency between efficient and Allocational Efficient Market market in which resource allocation bonds payments equal to its price the promised rate of return based Portfolio Variance utility curve is socially optimal on the current market price if bond is held to maturity and coupons Allocational efficiency the effectiveness with which a market are reinvested at same rate channels capital towards its most productive uses Information Efficient market market in which security prices YTM Example Asset Pricing ModelsAssumptions adjust rapidly to the arrival of new information Individual investors are price takers A capital market is said to be informational efficient if it Single period investment horizon immediately fully and correctly reflects all the relevant information Investments are limited to traded priced and perfectly divisible in determining security prices It is impossible to make economic financial assets profits by trading on the basis of that information setCovariance Example No taxes transaction costs or restriction on short sales Unlimited lendingborrowing at the riskless rate Investors are rational meanvariance optimizers Information is costless and available to all investorsIf a bond is sold between coupon payments part of the next Homogenous expectations ie same opportunity setsamecoupon payment belongs to the sellers accrued interest expected return variance and covariancefor all investorsCapital Market LineEfficient market hypothesis to what extent do securities marketsquickly and fully reflect different available informationThree levels of market efficiency This is known as the dirty or full price whereas a bond quoted 1 Weak form market level data without the accrued interest is known as the clean price prices reflect all past price and volume datatechnical analysis which relies on the past history of prices is of Bond Pricing with Fractional Period little or no value in assessing future changes in pricemarket adjusts or incorporates this information quickly and fully2 Semistrong form all public informationprices reflect all publicly available information For any single risky asset i within a welldiversified portfolio investors cannot act on new public information after its the unsystematic risk is diversified away the relevant total risk announcements and expect to earn aboveaverage riskadjustedIf we have a risky stockportfolio S defined by ER andsameasure in a welldiversified portfolio is the systematic risk returns Callable bond issuer has an option to buy back the entire bond at and a riskfree asset defind by R and0 then our fffs encompasses weak form as a subset call price portfolio P with w in S and 1w in riskfree asset then ss 3 Strong form all information both public and privateprices reflect all information public and private YieldtoCall Example1 Underpricedexpected returnrequired return according to no group of investors should be able to earn abnormal rates of CAPMlies above SML return by using publicly and privately available information 2 Overpricedexpected returnrequired return according to encompasses weak and semistrong forms as subsets CAPMlies below SML3 Correctly pricedexpectedrequired return to CAPMlies Weak Form Evidence along SML Test for independence randomness of stock price changesIf independent trends in price changes do not existCapital Allocation Line CAL Estimating the SMLReturn autocorrelation test Use the TBill rate as the riskfree rate Weak autocorrelation in individual stocks Use past market returns to estimate the expected market returns Strong autocorrelation in some portfolios Th

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