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1、9-19-29-39-49-59-69-79-89-99-109-119-129-139-149-159-169-17式中2 M為市場資產(chǎn)組合的方差； A 為投資者風(fēng)險厭惡的平均水平。請注意由于市場資產(chǎn)組合是最優(yōu)資產(chǎn)組合，即風(fēng)險有效地分散于資產(chǎn)組合中的所有股票， 2 M也也就是這個市場的系統(tǒng)風(fēng)險。9-189-199-209-219-22E(r)E(rM)rfM資本市場線CMLm9-23M 9-249-259-269-279-289-299-309-319-329-339-349-359-369-379-389-399-409-419-429-439-449-459-469-47E(r)E(rM
2、)rf證券市場線證券市場線SMLb bbM= 1.09-489-499-509-51E(r)Rx=13%SMLb b1.0Rm=11%Ry=7.8%3%1.25b bx.6b by.08By9-529-539-54QPZ(Q)Z(P)Erz (Q)Erz (P)E(r) 9-55),(),(),()()()()(2QPPQPPiQPQirrCovrrCovrrCovrErErErE任何資產(chǎn)的期望收益可以準(zhǔn)確地由任意兩個邊界資產(chǎn)組合的期望收益的線性函 數(shù)表示。例如，考慮有兩個最小方差邊界資產(chǎn)組合 P與Q，布萊克給出任意資產(chǎn)i的期 望收益的表達(dá)如下： The expected return of
3、any asset can be expressed as an exact, linear function of the expected return on any two frontier portfolios. Consider, for example, the minimum-variance frontier portfolios P and Q. Black showed that the expected return on any asset i can be expressed as9-56假定經(jīng)濟中只有兩個投資者，一個相對來說厭惡風(fēng)險，而另外一個可以忍受風(fēng)險。 厭惡風(fēng)
4、險的投資者選擇資本配置線上的資產(chǎn)組合 T，如圖 9-5所示，也就是說，他的資 產(chǎn)組合由資產(chǎn)組合 T與按無風(fēng)險利率貸出的無風(fēng)險資產(chǎn)組成。 T是由無風(fēng)險借貸利率 rf 出發(fā)的有效率邊界的切點。忍受風(fēng)險的投資者愿意在承擔(dān)更多風(fēng)險的前提下取得更高 的風(fēng)險溢價：他選擇圖中的 S。S資產(chǎn)組合與 T資產(chǎn)組合相比較，雖同處于有效率邊界 但其風(fēng)險與收益均高于 T 資產(chǎn)組合?？偟娘L(fēng)險資產(chǎn)組合（也就是市場資產(chǎn)組合，M ）由T與S結(jié)合而成，各自權(quán)重由兩個投資者的相對財富與風(fēng)險厭惡程度決定。由于 T與S 都在有效率邊界上，所以根據(jù)性質(zhì) 1，市場資產(chǎn)組合 M也在有效率邊界上。9-57Imagine an economy
5、with only two investors, one relatively risk averse and one risk tolerant. The risk-averse investor will choose a portfolio on the CAL supported by portfolio T in Figure 9.8, that is, he will mix portfolio T with lending at the risk-free rate. T is the tangency portfolio on the efficient frontier fr
6、om the risk-free lending rate, rf. The risk-tolerant investor is willing to accept more risk to earn a higher-risk premium; she will choose portfolio S. This portfolio lies along the efficient frontier with higher risk and return than portfolio T. The aggregate risky portfolio (i.e., the market port
7、folio, M) will be a combination of T and S, with weights determined by the relative wealth and degrees of risk aversion of the two investors. Since T and S are each on the efficient frontier, so is M (from Property 1).9-589-59根據(jù)性質(zhì) 2，市場資產(chǎn)組合 M 也存在一個在最小方差邊界上的零貝塔“伴隨”資 產(chǎn)組合： Z(M)，見圖 9-5。根據(jù)性質(zhì) 3及9-8式，我們可以用市
8、場資產(chǎn)組合 M及Z(M)來表 示任何證券的收益。由于 Cov(r M，r Z(M) )0，所以有From Property 2, M has a companion zero-beta portfolio on the minimum-variance frontier, Z(M), shown in Figure 9.8. Moreover, by Property 3 we can express the return on any security in terms of M and Z(M) as in equation 9.8. But, since by construction
9、Cov(r M，r Z(M) )0 , the expression simplifies to2)()(),()()()()(MMiMZMMZirrCovrErErErE9-602)()(),()()()()(MMiMZMMZirrCovrErErErE式中的資產(chǎn)組合 P與資產(chǎn)組合 Q分別由市場資產(chǎn)組合 M及Z(M)代替。上式可視為一個簡化了的 CAPM模型，在其中，E(r z (m) 取代了rf 。where P has been replaced by M and Q has been replaced by Z(M). Equation 9.9 may be interpreted as a variant of the simple CAPM, in which r f has been replaced with E(r z (m) 9-619-629-63f (ci) = 證券i 的流動溢價， f (ci) 是關(guān)于ci的一階單調(diào)遞增函數(shù)。 liquidity premium for security i9-64平均月收益率平均月收益率Average monthly return(%)買賣差價買賣差價Bid-ask spread (%)9-659-669-679-689-699-709-719-729-73
資本定價模型課件
