Equations for: Capital Market Expectations 2; Forecasting Asset Class Returns

LOS command words: All command words in this reading is “discuss“, with one “explain“. Discuss and explain both includes calculation abilities and questions, so all equations can be tested in calculation questions.

So which ones are essential? Unfortunately anything can be tested. As you go through the mocks you’ll see that some are tested more often than others but this isn’t a guarantee your exam will be representative of that.

Some candidates do decide to ditch this, but given that it can be tested in the essays, I wouldn’t just bin it.

Also, ’17 equations’ sounds terrifying but some of them aren’t calculation-centric. Let’s look through the equations and see.

Equation 1: The Grinold–Kroner model

Equation (1)

E(R_e)≈D/P+(%ΔE−%ΔS)+%ΔP/E

No getting around this one.

Equations 2-6: Singer-Terhaar model

Equations 2-6 is really an explanation of the various components of the Singer-Terhaar model, so that’s really all one concept, albeit an involved one.

Example 5 in the same reading would be a good one to go through.

Equations 7 & 8 – Capitalization Rates 

Equation (7)

E(R_re) = Cap rate + NOI growth rate.

Equation (8)

E(R_re) = Cap rate + NOI growth rate – %ΔCap rate.

These are variations of each other, where 7 is the long-run scenario and 8 is for scenarios with finite time horizons. And these aren’t really ‘equations’ so much as ‘you need to remember how expected return is calculated from capitalization rates’.

Equation 9: Capital Mobility

Equation (9) 

E(%ΔS_d/f) = (r^d – r^f) + (Term^d – Term^f) + (Credit^d – Credit^f) + (Equity^d – Equity^f) + (Liquid^d – Liquid^f)

Again, all this is saying is that you need to remember change in the exchange rate (%ΔS_d/f) will reflect the differences in the nominal short-term interest rates (r), term premiums (Τerm), credit premiums (Credit), equity premiums (Equity), and liquidity premiums (Liquid) in the foreign vs domestic markets. The equation is basically saying add up all the premiums and rate difference and you get your expected change in FX.

Equation 10-14: Covariance matrix

Yeah OK this is a lot of stuff to remember.

I would advice practicing questions and seeing which ones are needed. Remember that because of the essay questions CFA Institute can (and do) ask full questions based on specific areas.

Equations 15 & 16: Volatility from Smoothed Returns

I’d say Equation 16 is the key one here:

$var ( r ) = ( \frac{1 + \lambda }{ 1 - \lambda } ) var ( R ) > var ( R )$

Equation 17: ARCH models

Again, I’d say the concept behind it is more important. We had a recent discussion on ARCH models that you might like to refer to here.

Hope the breakdown makes it ‘7 concepts’ rather than ’17 equations’. Let us know how you get on with it!

I always appreciate your interpretation. We should analyze the main we become what we behold and necessary ideas.