# Grinold-Kroner model : repurchase yield

I am confused whether I should add or deduct the given repurchase yield.

For example, real earnings growth =4.5%

Inflation rate = 3.0%

Repurchase yield = - 0.5%

Dividend yield = 0.5%

Repricing return = 3%

So what could be the expected return?

11.5% or 10.5%.

deduct, but since in this case the yield is negative, it turns out positive.

Grinold Kroner

if Δ_S_ = the expected percent change in number of shares outstanding then

The term Δ_S_ is negative in the case of net positive share repurchases, so −Δ_S_ is a positive repurchase yield in such cases. Model itself says

• Expected income return: D/P − Δ_S._= 0.5 - (-0.5) = 1%
• Expected nominal earnings growth return: i + g.=3+4.5% = 7.5%
• Expected repricing return: Δ_PE.=3% given_
so net 11.5%
1 Like
1. By definition, repurchase yield is always negative as the objective is to reduce the number of ordinary shares outstanding in the market. So if we follow the G-K formula: Expected income return = Dividend yield - Repurchase yield = 0.5% - (-0.5%) = 1.0%
2. Alternatively you can think like this: If a company repurchase their shares outstanding from the market (kept as treasury shares for their company share performance scheme), what will happen to their expected rate of return on equity? Logically it should enhanced their return just as earning per share will be higher due to lower number of shares outstanding.
3. Conversely, an issue of new shares will mean a positive repurchase yield, as it increase the number of shares outstanding in the equity market, but it should reduce the expected rate of return on equity.

I agree with the comments here. I was under the impression that if they give you the repurchase yield and it’s negative, you would put it into the Grinold-Kroner equation with the negative sign and the net result would be a positive.

But then I did the 2009 past CFAI exam and it was the opposite. They give you the inputs for the GK equation, specifically:

Equity Repurchase yield = -0.5

Dividend Yield = 4.0

When asked for the Income return, which is the Div. Yield - (ΔS), they did:

4 - .5 = 3.5%

I did the opposite and ended up with 4.5% and got it wrong. Pretty frustrating way to get an answer wrong since the concept is very simple.

If the repurchase yield is -0.5 it means that the repurchase yield decreased. A decreased in the purchase yield should be deduct from the equation while a positive repurchase yield should be added.

If you repurchase shares (positive) it means that there’s less shares so you have a better return

It you decrease repurchasing shares (negative) like in this case, it means that you have a worst return.

This is correct, other comments are wrong.

Negative repurchase yield indicates an increase in number of shares outstanding - meaning it should be subtracted!

In the Grinold-Kroner model, you subtract %Δ_S_.

Note that,

repurchase yield ≈ −%Δ_S_

Therefore, if they give you the repurchase yield, you add it.

Voilà!

We must put the repurchase yield as given in the question

We need to reverse the sign if the changes in numbers of share is given.

Correct if i am wrong.

You add the repurchase yield (as given).

You subtract the percentage change in the number of shares.

I hope that you’re understanding why rather than simply trying to memorize it.

Thanks Magician.

You are the savior.

You’re welcome, and you’re too kind.

So correct answer would be 10.5%, right? Just to confirm that I am getting this right.

correct answer is whichever one that subtracts the 0.5% rather than adding it. So yes, 10.5% is correct. I feel like this question might have came from an old CFAI exam.

Thanks!!

Its from 2011 essay exam.