CAPITAL ASSET MARKET The reason for this convention can be clarified by an example. In many lotteries (in particular national lotteries), several tickets wear the same number. When a number is drawn, all tickets with that number receive identical prizes. Suppose all tickets have mean u and variance o of prizes. Then the expected yield on two tickets is clearly 2u, regardless of their numbers. But while the variance on two tickets is 2o when they have different numbers, it is 4o when they have identical numbers. If such lottery tickets are part of the available assets, we must therefore identify as many"different""assets as there are different numbers (regardless of the fact that they have identical means and variances). For ordinary assets such as corporate stock, it is of course known that although the yield is random it will be same on all units of each stock We shall denote the expected yield per unit of asset j by u; and the covariance between unit yield of assets j and k by ak. We shall also need the rather trivial gula ption that the covariance matrix for the yield of the risky assets is nonsin- An individual's portfolio can now be described as an n-dimensional vector with elements equal to his holdings of each of the n assets. We shall use x to denote individual i's holdings of assets j (after the exchange), and so his portfolio may be written(x1,x2,…,x) One of the purposes of the analysis is to compare the relations between the prices and yields of different assets. To facilitate such comparisons, it will prove useful to have a riskless asset as a yardstick. We shall take the riskless asset to be the nth. That it is riskless of course means that onk=0 for all k. But it may also be suggestive to identify this asset with money, and with this in mind we shall write specifically un=l, i.e., a dollar will(with certainty) be worth a dollar a year from now We denote the price per unit of asset by pi. Now, general equilibrium conditions are capable of determining relative prices only: we can arbitrarily fix one of the prices and express all others in terms of it. We may therefore proceed by fixing the price of the nth asset as g, 1. e,Pn=g. This means that we select the nth asset as numeraire. We shall return to the implications of this seemingly innocent con vention below ons and conventions, the expected yield on individual uitm and the variance (2)y2=∑∑oxx As mentioned earlier, we postulate for each individual a preference ordering has content downl ued stube to sT oR ems aecondtp23013020-0 AMCAPITAL ASSET MARKET 771 The reason for this convention can be clarified by an example. In many lotteries (in particular national lotteries), several tickets wear the same number. When a number is drawn, all tickets with that number receive identical prizes. Suppose all tickets have mean M and variance a2 of prizes. Then the expected yield on two tickets is clearly 2ji, regardless of their numbers. But while the variance on two tickets is 2a2 when they have different numbers, it is 4a2 when they have identical numbers. If such lottery tickets are part of the available assets, we must therefore identify as many "different" assets as there are different numbers (regardless of the fact that they have identical means and variances). For ordinary assets such as corporate stock, it is of course known that although the yield is random it will be the same on all units of each stock. We shall denote the expected yield per unit of assetj by jt3 and the covariance between unit yield of assets j and k by ai k- We shall also need the rather trivial assumption that the covariance matrix for the yield of the risky assets is nonsin￾gular. An individual's portfolio can now be described as an n-dimensional vector with elements equal to his holdings of each of the n assets. We shall use xJ to denote individual i's holdings of assets j (after the exchange), and so his portfolio may be written (xl, xi, ..., xi). One of the purposes of the analysis is to compare the relations between the prices and yields of different assets. To facilitate such comparisons, it will prove useful to have a riskless asset as a yardstick. We shall take the riskless asset to be the nth. That it is riskless of course means that ank = 0 for all k. But it may also be suggestive to identify this asset with money, and with this in mind we shall write specifically Pun=1, i.e., a dollar will (with certainty) be worth a dollar a year from now. We denote the price per unit of assetj byp,. Now, general equilibrium conditions are capable of determining relative prices only: we can arbitrarily fix one of the prices and express all others in terms of it. We may therefore proceed by fixing the price of the nth asset as q, i.e., P n = q. This means that we select the nth asset as numeraire. We shall return to the implications of this seemingly innocent con￾vention below. With the above assumptions and conventions, the expected yield on individual i's portfolio can be written: n-I (1) Y1 L tjxi+Xn j=i and the variance: n-I n-i (2) Y2 =i x jaX Xaa j=1 a=1 As mentioned earlier, we postulate for each individual a preference ordering This content downloaded from 202.115.118.13 on Wed, 11 Sep 2013 02:20:50 AM All use subject to JSTOR Terms and Conditions