QandA 3.11

[Canuck_Act]

Hello All!

I have a question re QandA question 3.11

If the asset's income was in the form of a continuous dividend rate, q, applied to the asset (and then reinvested in the shares/asset), then would not the value of the asset at some future time reflect all the income that has been earned by the asset over the time period?

That is, asset value at time zero = 4400. At time, T, asset value is 4800.
So, if he income is earned on a continuous divedend basis and re-invested in the asset, then does not the asset value at time T already reflect the income that was earned over that period? (As well as the capital gain)

Thanks, in advance!

Cheers!

 

[Colin McKee]

Income reinvestment

This is tough. I am not 100% sure what you are saying here. The price of any asset could be said to be the reflection of all future income for all time periods in the future. The change in the assets price is the change in the discounted value of that icome or a re-assessment of the amount of the income. But the key for pricing a future is that we are not estimating the expected value of the asset at time T. The task of assessing the assets value is left to the market price. We are only looking at the two different ways of buying the asset - either now with cash, or later in forward contract. So its only the missing income that affects the difference between the two prices.

 

[Canuck_Act]

Hi Colin!

Thanks for the reply.

What I was puzzled about was the part of the answer, after the main part, (That is, after comparing the returns on the two investments, which seemed perfectly acceptable to me) where they try to assess the performance including the income "earned".

In my view, the income earned on the asset comes from the constant dividend yield earned on, and reinvested back in, the asset. Hence, its income earned over the time period is reflected in the asset's price (which will also reflect any capital gain/loss) at the later time.

Note: My reasoning here only applies to assets where the income is earned on a continuous dividend yield, and then contiunously reinvested back into the asset. So, the asset value at time T, reflects the income earned (via the continuous dividend) on the asset.

Then total return between t and T = {V(T-t) - V(t)}/V(t)

Thanks again

 

[Colin McKee]

income reinvestment

Hi,
You say that the income earned over the time period is reflected in the asset price. But I view it that the asset price reflects the view only of income to be earned in the future, and the value of that can change without warning. The income earned in the past is largely irrelevant to the asset price. So if I have a discount rate of 5% (continuous) and expect a constant continuous dividend of 10p pa, I would expect the share to stand at 200p = 10p/0.05. In a year's time I will have received the 10p dividend, but if the markets perception of the growth in the dividend or the discount rate to use in valuation of the asset have changed, then the share price could be anywhere. If the assumptions are unchanged the share price will still be 200p. If I had re-invested my dividend continuously my investment would be worth 200p * exp (0.05 * 1) = 210.25p. This would be the assumption used when pricing the future at time 0.
So, returning the Q&A question, I dont get the link between the share price at time 3 months, and the past income received (and reinvested in) the share. The key for me is that the price reflects future expectations, and not past income received (unless we assume that all market assumptions remain constant.

 

[Canuck_Act]

Hi Colin!

Thank you for your reply.

I agree with your take on the valuation of an asset.

However, my question concerns issues where we are asked to compare assets (or more accurately to compare the returns on an assets).

So, if the asset in question is, say, an equity market index, which pays a continuous dividend, at rate q, which is immediately reinvested back into the index as it is received, then does not the change in index value, over time period t to T, also reflect the income earned on the index in the time period?

If so, then to determine total return earned between time t and time T, we simply use:

{I(T-t) - I(t)}/ I(t) ,

where I(s) is the value of he index at time s.

If not, then I'll re-read that section of the course.

Thanks again.

 

[him27jan]

Hi Canuck_Act

Let me try to clarify your doubt.

See if you have got dividends and you are re-investing it, it will not increase the UNIT price of the asset but it will increase the TOTAL valueof the asset you have HELD (i.e. UNIT price X Quanity of the Asset) since quanity of the asset held has increased due to the purchase of the asset from the money received through dividends.

Keeping this in the mind, in the question reference, the unit price of index is 4400 at t=0. During the 3 months period you have received approximately 35 as dividends. Now assuming you have received dividends at t=3 months you would have additional 35/4800 units of index i.e. 0.007292 units. Hence, the total units you will have of index is 1+0.007292 = 1.007292.

Now at t=3 months, the UNIT price of the index is 4800 which factors the future income to be received. However, the total asset value is 4800 X 1.007292. Thus TOTAL RETURN on index for 3 months is [4800X1.007292-4400]/4400% which is 9.9% approx. and hence the answer also in the solution given to the question.