International CAPM/Singer–Terhaar approach

In finance there are several approaches used to explain the relationship between risk and return in captial markets. Such theories are called financial equilibrium models and include the Black–Litterman approach and the international CAPM–based approach presented in Singer and Terhaar (1997).

Many of us are familiar with the traditional CAPM model frequently used to estimate the cost of equity. The international CAPM is simply an extension of this approach that tries to take into account barriers to capital mobility globally which is coined as the degree of market integration.

For those of us interested in the method used in the ICAPM - the approach is as folows:

Recall the two key formulae:

1. Risk Premium Asset = Corr (Asset, Market) x Risk Premium Market x std asset / std market = Corr (A,M) x SR (M) x std asset 
(perfectly integrated markets risk premium

This first formula comes from the original CAPM formula E(r) = rf + beta x (rm-rf) and is arrived by rearranging it. Note beta asset = Cov (Return asset, Return Market) / Var (Return Market)


2. Risk Premium Asset = Risk Premium Market x std asset / std market = SR (M) x std asset
(completed segmented markets risk premium)


Once we have the formula we can then apply them to estimate the expected equity return for an asset taking into account an assumed degree of integration.

Example:

Say we assume the following:

a) degree of integration = 80%
b) asset expected standard deviation = 7%
c) sharpe ratio of the market (global investable market/GIM) = 0.28
d) correlation of the asset to the market = 0.54


Risk Premium Asset (eq 1) = 0.28 x 0.54 x 7 %  = 1.06%
Risk Premium Asset (eq 2) =  0.28 x 7 % = 1.96%
Overall Risk Premium Asset = 0.8 x 1.06% + 0.2 x 1.96% = 0.392% + 0.848% = 1.24%

Assuming a risk free rate of 5% we get the Singer–Terhaar approach expected return of:

5%+ 1.24% = 6.24%

The calculation could also include a liquidity premium manifesting itself in an extra return for lower liquidity. It will therefore be added to 6.24%.

It is worthwhile also to recall the formula:

Cov (A,B) = beta (a) x beta (b) x variance of the market




Note: formula and example based on the CFA 2018 study materials

Build-up Approach

When it comes to bond investing, there is multitude of conceptual ideas worth looking at. One I recommend is the build up approach AKA the risk premium approach.

What it does it really break down the expected return into components and I think its worth while understanding what these components are to get a feel for the compensation you as an investor are receiving for the various risks inherent in the security:

Expected Return on the Bond = Real risk-free interest rate + Inflation premium + Default risk premium + Illiquidity premium + Maturity premium + Tax premium

This formula essentially breaks down the various risks into components with most of them self explanatory.

For most investment grade bonds the key ones are:

a) the inflation premium which is essentially the return you would expect to generate as compensation for both current inflation to maturity and the risks associated with uncertain inflation into the future until maturity.

b) maturity premium - there is always some risk that the maturity is extended some years into the future and that interest rates rise during that future uncertain period. this premium compensates for this.

As we look at securities today and evaluate them across multiple asset classes, I think it is really worth looking at them from the perspective of this build up approach to understand where the risks could be.

For example with many junk yield US bonds there could be or should be a significant maturity premium attached as not only these speculative issuers are likely to restructure their bond liabilities extending the repayment periods but also the US interest rates rising over time could mean that bond investors get hit as overlevered issuers are unlikely to be in a position to increase coupon rates while higher rates will likely mean better yielding alternatives will be available for investors.

I would think of this as a high yield trap of sorts as the investor loses twice, first on this opportunity cost in an up market (when rates rise & issuers restructure) but at the same time if the economy enters a recession credit spreads will increase on high yield fixed income and prices will fall.