FIN 720 Mod 1 Ch 1-4 notes.docx - Chapter 720-1 Some Basic...

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Chapter 720-1 Some Basic AlgebraChapter 720-2 Risk and Return in the Context of Market Equilibrium (same as 710)Financial assets vs. real assets:Financial assets:Securities: stocks, bonds, preferred stocks, etc. Contracts: options contracts, forward contracts, futures contracts, etc. Real assets:machines, equipment, properties, production lines (projects), etc.A portfolio comprised of single assets is also an asset.Every asset, financial or real or a portfolio, has a market value. The market value changes overtime. The future value of the asset is uncertain; therefore, there is a risk. Definition of key symbols:E(R):Expected rate of return of an assetR:Required rate of return of an assetσ2(R):Variance of an assetσ(R):Standard deviation of an assetρ(RA ,RB): Correlation coefficient between two assets A and B β: Market risk index of an assetEx-ante:before the fact; that is, the outcome of the event will occur in the future and is unknown at the present time.Ex-post:after the fact; that is, the outcome of the event has already become historical data. 1.Expected rate of return of an asset for the period,E(R)E(R)=E(P1)+E(AI1)−P0P0(1)E(R)= Expected rate of return of the asset for the periodE(P1)= Expected price (value) of the asset at the end of the period, t=1E(AI1)= Expected additional income from the asset during the period or at the end of the period, t=1P0= Market Price (value) of the asset at the present time, t=0Assume that there are three possible economic conditions in the coming period, good, average, and bad. The probability for each condition to occur and the corresponding price and additional income of the asset are assessedand shown in the following table. Assume that current asset price (that is, the price at time 0), P0, is 37. P1,iis the asset price at time 1 (that is, at the end of the period) under economic condition i, and AI1,iis the additional incomereceived during the period or at time 1 under economic condition i. Current asset price (P0)37Economic condition (i)Good (i=1)Average (i=2)Bad (i=3)[1]
Probability (xi)0.30.50.2Asset price at time 1 (P1,i)403736Additional income (AI1,i)322E(P1)=Expected asset price at time 1¿i=1nxi(P1,i)=x1P1,1+x2P1,2+x3P1,3=.3(40)+.5(37)+.2(36)=37.7E(D1)=Expected additional income received during the period¿i=1nxi(Ai1 ,i)=x1AI1,1+x2AI1,2+x3AI1,3=.3(3)+.5(2)+.2(2)=2.3E(R)=E(P1)+E(AI1)−P0P0=37.7+2.33737=.0811The time period can be one day, one week, one month, one quarter, one year, and so on. In this class we use one year as the period, unless otherwise specified. The method shown above is based on ex-ante approach; that is, based on possible future economic conditions, their probabilities, and the corresponding cash flows (future asset prices and additional income). But future cash flows and the probabilities are difficulty to assess. So this approach is difficult to use. Later in this chapter, we willshow an ex-post approach; that is, based on historical price and income data. For a common stock, the additional income is dividend. For a bond, the additional income is coupon payment.

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