Portofolio Capm

III. Asset Pricing Models CAPM Capital Asset Pricing Model 1964, Sharpe, Linter quantifies the risk/return tradeoff

assume investors choose risky and risk-free asset no transactions costs, taxes same expectations, time horizon risk averse investors

CAPM membutuhkan beberapa asumsi seperti adanya suatu asset bebas resiko (non saham) dan semua investor mempunyai tipe utilitas dan ekspektasi yang sama. Capital market line (CML) mengilustrasikan hubungan linear antara Ekspektasi return suatu portfolio dan standard deviasinya, ketika portofolio tersebut terdiri dari suatu kombinasi portofolio pasar dan asset bebas resiko.

Daripada memilih portofolio C, investor diasumsikan memilih portofolio M. Garis FM, dikenal sebagai Capital Market Line, punya gradient {E(RM) – Rf}/σm and intercept Rf.

Ketika seorang investor mengkombinasikan portofolio pasar dan asset bebas resiko, maka nilai harapan returnnya adalah: E(Rp) = expected return of the portfolio E(RM) = expected return of the market Rf = The risk free rate σP = the standard deviation of the portfolio returns σM = the standard deviation of the market returns

Perhatikan suatu portofolio S, terdiri dari single aset beresiko i dan portofolio market M. Misalkan w bobot investasi di i dan 1-w bobot investasi di M. Sekarang lihat plot E(Rs) dan σs. Gradien garis risk-return adalah Sekarang kita lihat bahwa

Selanjutnya kita lihat, Jika diset w = 0,

Gradien garis portofolio tersebut adalah Dari sebelumnya kita tahu bahwa gradien portofolio pasar adalah [E(RM)-Rf ]/σM

Akhirnya diperoleh

Dengan manipulasi aljabar, diperoleh hubungan yang sangat terkenal sebagai berikut : Beta (β) adalah perbandingan atau ratio σi,M / σM,M , Note that the beta of the market portfolio is equal to 1. Persamaan (12.18), dikenal sebagai Securities Market Line, merupakan hasil utama dari CAPM.

Example Kita ilustrasikan betapa sederhana menggunakan formula CAPM untuk menghitung nilai harapan return. Misalkan rf = 8%. Rata-rata return pasar mempunyai nilai harapan (rM) 12% dan standard deviasi (σM) 15%. Ada suatu asset yang mempunyai covariance terhadap pasar (σiM) 0.045. Selanjutnya dapat dihitung nilai dari   β = 0.045/0.152 = 2. Sedangkan nilai harapan return asset tersebut adalah ri-bar = 0.08 + 2(0.12-0.08) = 16%.

Example. What will be the expected rate of return on AAPL stock with a beta of 1.49 if the risk-free rate of interest is 2% and if the market risk premium, which is the difference between expected return on the market portfolio and the risk-free rate of return is estimated to be 8%? AAPL expected return = 2% + 1.49*8% = 13.92%.

Nilai β menggambarkan hubungan antara nilai harapan return suatu asset dengan nilai harapan return pasar. Makin tinggi nilai β, makin besar hubungan asset dengan pasar. Jika suatu sekuritas cenderung bergerak pada garis pasar, σim sama dengan σm2 sehingga nilai β = 1. Suatu sekuritas dengan nilai β > 1 sering dikatakan aggressive, sedangkan suatu sekuritas dengan nilai β < 1 sering dikatakan defensive.

interpreting b if b = 0 asset is risk free if b = 1 asset return = market return if b > 1 asset is riskier than market index b < 1 asset is less risky than market index

Example Suppose we have the following data about company j and the market portfolio m. j = 10%; j,M = 0.70; M = 5%. Calculate the systematic risk of company j Cov(Jm) = std of j x std of M x correlation of j and M = 0.1 x 0.05 x 0.7 = 0.0035 Therefore j = 0.0035/0.052 = 1.40

Sample betas (monthly returns, 5 years back)

measuring b estimated by regression data on returns of assets data on returns of market index estimate

Example Suppose that the risk free return on the market portfolio is 12% and the beta value of a share in the ABC company is 1.30. Calculate the return on ABC share using CAPM. Using the equation above: E(rj) = rf + βj(rm – rf) = 5 + 1.30(2 -5) =14.1%

Portfolio Beta: Example Suppose we had the following investments: Security Amount invested Expected Return(%) Beta Stock A $1,000 8 0.80 Stock B $2,000 12 0 .95 Stock C $3,000 15 1.10 Stock D $4,000 18 1.40 What is the expected return on this portfolio? What is the beta of this portfolio? Does this portfolio have more or less systematic risk than the average asset?

Solution Calculate the portfolio weight: Total amount invested is $10,000. A = 10%, B = 20%, C = 30%, D = 40% Expected return = .10 x 8% + .20 x 12% + .30 x 15 + .40 x 18% = 14.9 Portfolio beta = .10 x .80 + .20 x .95 + .30 x 1.10 + .40 x 1.40 = 1.16 Beta is larger than 1, this portfolio has greater systematic risk than an average asset.