I’m interrupting my book review to continue an interesting discussion over at Canadian Financial DIY (post 1 and post 2). The posts and follow-up comments make good points about investor psychology, but I’m more interested in getting the right answer for rational investors.
A quick search turned up a useful paper by John Norstad. This paper describes all the math I needed to calculate optimal portfolios, and it provides information about stock and bond returns in the US from 1926 to 1994.
The paper assumes that you can borrow at a rate that is 0.83% above inflation. Based on all this, I worked out the optimal mix of borrowing, stocks, and bonds to maximize the expected compound return. Let’s assume that you have $100,000 to invest.
Drum roll, please! The optimum portfolio has you borrowing $180,000 (for a total of $280,000 to invest now), and investing $196,000 in stocks and $84,000 in bonds. This mix gives you a boost of 2.45% per year over an all-stock portfolio with no borrowing. Wow, that was anticlimactic.
Does this mix of investments sound crazy to you? It seems way too risky to me. How can it make sense to borrow so much money? We’re assuming that you will rebalance your portfolio frequently to maintain the right proportions, but any quick drop in stock prices would really hurt.
The problem with this analysis is the assumed borrowing rate. Who can borrow at less than 1% above the current inflation rate? What happens if we change this to assume that we can borrow at a rate that is 2% above inflation?
I went back to Excel with this new borrowing rate. The result is that you should borrow $70,000, put $170,000 into stocks, and put nothing in bonds. Now you’re getting only a 1.01% per year boost over an all-stock portfolio with no borrowing.
That’s quite a difference from the first portfolio. What happens if the borrowing rate is even higher than 2% above inflation? All that happens is that the amount borrowed drops. The optimal portfolio still has no bonds. When we get to a borrowing rate that is 5% above inflation, there is no borrowing, and the whole $100,000 goes into stocks.
All analyses like this one have built-in assumptions that need to be examined. The main message here is that the interest rate on borrowed money makes a huge difference in how you should invest. A secondary message is that I’m still searching for a rational reason to invest in bonds for the long term.