The required return on equity, R

Required return on equity, or R, is an important building blocks for stock’s valuation. It is used in various valuation model i.e. DCF and other relative value method (i.e. P/E and P/B method).

Due to its importance, I have been searching for methods that produces a reliable result and is practical in term of availability of input data and simplicity of the model. After review of the CFA curriculum and online materials, I came across works done by Aswath Damodaran, a Professor of Finance at the Stern School of Business at New York who is teaching valuation and corporate finance in MBA programs. He was named by Business Week, in 2011 as the most popular business school professor in US. In his “Equity Risk Premiums(ERP): Determinants, Estimation and Implication (2013)”, he presented a number of methods to compute the ERP, which is one of the inputs for Capital Asset Pricing Model (CAPM), a popular model to determine the R. Besides his work on ERP, his website also provided an extensive range of data to facilitate the computation of ERP.  

Before detailing my selected method, I will give a list of general choices in determining R as below.

           A.   CAPM

Required return on stock i, R_i = Risk-free return, R_f + β_I (ERP)

               B.   Fama-French Model (Multifactor Models)

                              R_i = R_f + β^market RMRF + β^size SMB + β^valueHML

RMRF: R_m - R_f (Return on market (i.e. FBMKLCI) – Risk-free return)

SMB: Small minus Big (Return of SmallCap Portfolio – LargeCap)

HML: High minus Low (High Book/Price – Low)

           C.   Build-up Method

 R_i = R_f + ERP ± Risk Premia₁ ± Risk Premia_{2 ±} ……. ± Risk Premia_n

I will use the CAPM to compute R because

(i)                  it requires fewer inputs compare to the method B and C

(ii)                input data is more available (compare to, say, B that require return on SmallCap portfolio like FBMSmallCap, return data on FBMKLCI is more easily available)

(iii)               Damodaran’s site provide updated data for the computation of ERP, which is less work for me

Hence,

R_i = R_f + β_I x ERP

where:

R_i = Required rate of return of stock i

R_f  - Risk-free rate of return. Represented by Malaysia 5-Years or 10-Year Govt Bonds Yield depending my selected time-horizon

ERP =Equity Risk Premium for investing in the market(FBMKLCI), relative to the risk-free rate

Β_i – Beta of stock i against market. To obtain via regression analysis of FBMKLCI and stock’s return data

Method for the inputs are described above but ERP’s is following.

In his work, Damodaran explained that ERP for a country’s market can be obtained by, first, calculate the ERP of a matured market like US as the base. Then, a Country Risk Premium (RP) is added to the base for the additional risk.

ERP = Base ERP for mature market + Country RP

Based ERP is obtained by a method called Implied ERP. On a brief note, the Implied ERP is obtained by solving the R(required return) for the latest S&P500 year-end closing given an estimated future dividends growth. I will use the data provided by his site as I believe his work is reliable and the computation (if I choose to compute myself) is too data-intensive for me.

(Other that the Implied ERP, one can also use the historical ERP. It is can be obtained by subtracting Average Return of S&P500 with Average Return of T.Bond over a certain period of time. However, this method is backward-looking. A forward-looking method like the Implied ERP is more relevant)

For the Country RP, I will use the Melded CDS approach (describe in his work).

Country RP = Malaysia CDS Spread x Relative Standard Deviation (Equity Market/Bond Market)

The first term of the formula is the 5 years Credit Default Swap(CDS) rate of Malaysia (or 10-years, depending on my selection). It is the required rate of return for investors to provide insurance against the risk of sovereign debt default and the latest rate can be obtained from the Deutsche Bank Research website. The higher the CDS, the higher the probability debt default by Malaysia’s government. As the CDS only represent the risk of sovereign’s bond default, we need to covert the bond’s risk premium to equity risk premium. Hence the second-term is used, which is the relative standard deviation (or risk) of the equity market(FBMKLCI) vs bond market. In this case, I will used the data provided by Damodaran, which are based on 2 years weekly data.

(Alternatively, the CDS can be replaced by Moody’s Rating-based default spread according to Malaysia’s sovereign rating. It is more stable and do not change frequently compared to CDS, which is determined by the market and is fluctuating daily. As CDS is usually higher than default spread and it imply all the market’s expectation, I choose CDS as a conservative approach and most relevant to the current situation. )

In conclusion,

R_i = R_f + β_I x [Implied ERP_US  + (CDS Spread_Malaysia x Relative S.D.)]

  

ERP of US Market (1-Jan-15)	5.75%
Malaysia 5-years CDS (22-Jan-15)	1.3115%
Relative σ (2 years weekly data)	1.27
ERP	7.416% (5.75% + 1.27 x 1.3115%)
Malaysia 5Y Bond Yield (22-Jan-15)	3.811%

Hence, R_i = 3.811% + β_I x 7.416%

For example, the R of FBMKLCI (β = 1.0) is 11.227%.

The application of the R, for example, is as below. We can extract market expectation on the current FBMKLCI level, based on Gordon growth model

                P₀ – 1803.08 (23-Jan-15)

                E₀ – 106.37 (estimate)

                D₀ – 59.354

                R – 0.11227

Solving the formula, I get g = 0.0768 (7.68%). The market is expecting FBMKLCI to have a constant growth rate of 7.68% (if based on Gordon Growth Model).

Reference: http://pages.stern.nyu.edu/~adamodar/