# Income return in Grinold-Kroner model

Made a mistake in a mock review that’s been bugging me because I made the same mistake 2 months ago…

The income return = div yield + repurchase yield

Is it safe to say that we should add whatever value of the repurchase yield is given?

E.g: if the repurchase yield is -2%, div yield is 3%, then the income yield is 1%.

If the repurchase yield is 2%, div yield is 3%, then income yield is 5%.

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The other way around. Negative repurchase yield increases income return, v.v.

It was a long shot, glad i made it.

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Equity compounded annual growth rate (%) 11.2

Equity risk premium (%) 5.3

Dividend yield (%) 4.0

Equity repurchase yield (%) –0.5

Nominal earnings growth return (%) 4.6

Current and Forward Looking Data

Current equity price-to-earnings ratio 14.6

Expected equities real earnings growth rate (%) 2.7

Expected long-term inflation rate (%) 2.5

Solution:

Income return is the sum of the dividend yield (i.e., D/P, which is 4.0%) and the equity

repurchase yield (i.e., the negative of the expected change in shares outstanding, - ΔS)

which is -0.5%. Therefore:

Income return = D/P - ΔS = 4.0 - 0.5 = 3.5%

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Btw this is from 2009 AM, question 5

that is incorrect. Negative repurchase yield is more shares issued.

So 3.5 is the suggested answer?

It was a long shot, glad i made it.

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Yea Epsilon that’s the same mistake I made. Go correct your notes like I did v.v

The way i understand it is the formula for the change is:

End - Beg / Beg; so a negative means more repurchases thus increases income return.

Which part is incorrect?

It was a long shot, glad i made it.

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If the company BUYS back shares it will lower the required return on the stock (hence the negative value for this coefficient in the model). If they ISSUE more shares then the investor will require a higher return on the stock.

just remember that two negatives make a positive.

¯\_(ツ)_/¯ It be like that sometimes.

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^ that’s also wrong.

If they issue more shares –> repurchase yield negative –> dilution –> lower expected return. Grinold-Kroner is a expected return model, not required return model.

In the exam they’ll either give us the repurchase yield (easy because they’ll give the sign, just add it to the equation), or the %change in shares. If the %change in shares is negative (say -3%), then we add 3%. if the %change is positive (3%), we subtract 3%.

Nah, a buyback increases return and issuing shares decreases return. U got it backwards ;)

exactly. A simple equation, Grinold-Kroner, can actually be very tricky and half the takers will lose poimts

Agree that a buyback increases return and it implies a negative change in the outstanding shares (ending < beginning). Is it not?

It was a long shot, glad i made it.

you r correct. when they give positive repurchase yield, they r giving you a negative change in shares outstanding

Got it. I misconstrued repurchase yield and change in outstanding shares. Thanks

It was a long shot, glad i made it.

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Even though this thing is pretty much take care of, you could apply a bit of corporate finance here to understand better. If % of shares outstanding next year is gonna fall by say 2%, it means there is buyback which is similar to a dividend and adds value fo investors. In turn leading to a higher return for investors. If shares outstanding increase, the company duping its overvalued shares on to investors and would not add much value and hence lower returns.

I’m too tired to understand the above thread. Could we summarize it in the simplest way?

positive repurchase yield = repurchase ==> less shares ==> more expected returnnegative repurchase yield = issuance ==> more shares ==> less expected returnIs this OK?

Yes, but don’t get mixed up when you see the formula, which is: Dividend Yield - share repurchase yield

So when you say positive repurchase yield, yes this does increase the return (and added to the dividend yield) but if you simply plug in the number into the equation above you’ll be subtracting the repurchase yield from the dividend yield.

So it comes down to how they phrase the question: “Reduction in shares outstanding = 4%” is the same thing as saying “repurchase yield = 4%”.

Bottom line: When # of shares is decreasing or the repurchase yield is positive you add this number to the dividend yield. Vice versa for increasing number of shares.

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Positive change in shares = dilution = Negative repurchase yield

Negative change in shares = repurchases = positive repurchase yield

That is all.

Nice, thanks

the value of the expected income return = d1/p0 - (Change in shares outstanding).

if they say repurchase yield = (anything positive here), this is a negative value as shares outstanding declines.

you would have a div yield of 4% - (-2% change) or a 6% value. only if shares outstanding grow will your income value decline.

Don’t forget that the expected earnings growth is a nominal value as well and you need to add the inflation figure to it.

this calculation will take out several people, maybe even myself.

"excluding the effects of the significant events described above....'

the value of the earnings growth is real thats why you still have to add the inflation figure

It was a long shot, glad i made it.

got you. yes, i meant that line item, expected earnings is nominal. the earnings growth is real + the value of inflation. thanks.

"excluding the effects of the significant events described above....'

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I fixed my thinking.

¯\_(ツ)_/¯ It be like that sometimes.