While calculating the forward price of securities with known dividend yields, the text mentions that the when the dividend payments are a percentage of the price, then it is assumed that the income from dividends is reinvested...Else, in the case of cash payments, it is assumed that the income is invested in a risk free security.
The notes explain that in the former case, it is easier because we will know the amount of stock that we will purchase. In the latter, it says that it is not possible to know the amount of stock that we will be able to purchase with the dividends.
My question is what difference does it make? Even if we do not know the amount of equity I am purchasing, why cannot we ahead and assume that the dividend will be reinvested? I mean...sure, we will not know how much of additional equity we have purchased, but since we are reinvesting our dividends, wont it be a smart play?
"The important principle for this case and the known income case is that, if the
income is proportional to the underlying security, S, we assume the income is
reinvested in the security. If the income is a fixed amount regardless of the price
of the security at the payment date, then we assume it is invested in the risk-free
security. This is because when the payment is proportional to the stock price
(eg dividends) we know how many units of stock they will purchase, but we do
not know how much cash is paid (as the stock price is unknown). So we can
predict the amount of stock held at the end if we assume reinvestment in the
stock.
With a cash payment on the other hand, we would not know how much stock
could be bought, but we do know how much the cash would accumulate to at the
risk-free force of interest. Assuming dividends are reinvested in the security, but
cash is invested at the risk-free (and known) force of interest enables us to
predict the final portfolio without requiring any information about the price of the
asset S during the course of the contract"
The notes explain that in the former case, it is easier because we will know the amount of stock that we will purchase. In the latter, it says that it is not possible to know the amount of stock that we will be able to purchase with the dividends.
My question is what difference does it make? Even if we do not know the amount of equity I am purchasing, why cannot we ahead and assume that the dividend will be reinvested? I mean...sure, we will not know how much of additional equity we have purchased, but since we are reinvesting our dividends, wont it be a smart play?
"The important principle for this case and the known income case is that, if the
income is proportional to the underlying security, S, we assume the income is
reinvested in the security. If the income is a fixed amount regardless of the price
of the security at the payment date, then we assume it is invested in the risk-free
security. This is because when the payment is proportional to the stock price
(eg dividends) we know how many units of stock they will purchase, but we do
not know how much cash is paid (as the stock price is unknown). So we can
predict the amount of stock held at the end if we assume reinvestment in the
stock.
With a cash payment on the other hand, we would not know how much stock
could be bought, but we do know how much the cash would accumulate to at the
risk-free force of interest. Assuming dividends are reinvested in the security, but
cash is invested at the risk-free (and known) force of interest enables us to
predict the final portfolio without requiring any information about the price of the
asset S during the course of the contract"
