16th letter to friends of Brunei [Portfolio Management (Part 3)]

Our study of portfolio management will lead us to one common sense question: What if I can invest in a risk-free asset, how much more (risk premium) should I get if I were to invest in a risky (of various degree) assets. In US, the risk-free asset is usually the T-bill issued by US government. In Singapore, it can refer to FD rate, CPF rate or Singapore government 10 year bond.

This question leads to a development of an important equation (known as CAPM: Captial Asset Pricing Model):

Expected Return (of a stock) = Risk free Return (Rf) + Risk Premium

where Risk premium = β (Rm – Rf)

[β(beta) = sensitivity of a stock to a market index; Rm = Expected Market Return]

Let's do an example: Mr. Tan is considering investing in a stock of DBS. Tan expects market return for bank's stock to be 14%. DBS's beta is 1.4 (on STI), a risk free Singapore government 10 years bond return is 3%. Calculate the expected return on DBS stock.

E (DBS) = R(f) + β (Rm – Rf )

E(DBS) = 3% + 1.4 (14% - 3%) = 18.4%

Another example: The return of DBS is 16%, the market return for bank's stock is 14.2%, risk-free S'pore 10 year bond is 3%. Determine the beta for DBS.

a. 0.65

b. 0.91

c. 1.42

d. 1.16

* Working: E (DBS) = R (f) +β (Rm – R f)

16% = 3% + β (14.2% - 3%)

(16% -3%) / (11.2%) = β

β = 1.16

I.e. When STI rises (or drops) by 1 %, DBS stock will rise (or drop) by 16% over and above STI.