Question

You are considering investing in the SPY Exchange Traded Fund.   This fund delivers returns that closely track the S&P 500 Stock Index. While the rate of return that the SPY will deliver in the future is uncertain, the mean or expected return is 7% per year.   Your initial plan was to invest $50,000, using your own money.   However, your broker says that she will loan you another $50,000 at a 4% interest rate, thereby allowing you to invest $100,000 in the SPY. (Just as an FYI, this is known as purchasing stock on margin).

The following questions can be answered conceptually without numbers, though it is possible to supply numbers if you wish.

1. Is the expected rate of return on your $50,000 personal investment larger with or without the loan from your broker?
2. Assume that the market does unexpectedly well, for example delivering a return of 25%.   Is the rate of return on your $50,000 personal investment larger with or without the loan from your broker?
3. Assume that the market does unexpectedly poorly, for example delivering a return of -25%.   Is the rate of return on your $50,000 personal investment larger with or without the loan from your broker?
4. Summarize the general principle at work here.

Answer 1

a).

Our expected return from SPY is 7%. We took the loan at 4%. So, we would have earned 7% on our 50000 investment. Now, we are earning another 7% on another 50000 with the borrowing cost of just 4%, which will be our additional return. So, the expected rate of return on our personal investment is larger with the loan from the broker.

b).

Given that the market does unexpectedly well and return is 25%. So, along with the earning of 25% of our investment of 50000, we earned another 25% on the borrowed 50000 with a borrowing cost of just 4%. So, the rate of return on our personal investment is larger with the loan from the broker.

c).

Given that the market done unexpectedly poor and return is -25%. So, along with the loss of -25% on our investment, we lost an extra 25% on the borrowed 50000 along with the borrowing cost associated with it. So, the rate of return on our personal investmeng is larger without the loan from the broker.

d). The general principle here is, if the rate of return is greater than the borrowing cost, it is advisable to go for purchasing stock with margin, as it will result in greater effective rate of returns on our investment. If the rate of return is less than the borrowing cost, the losses will get intensified and the rate of returns will be much lesser which can erode the capital in worst cases.