A quick search turned up the useful paper

*Portfolio Optimization*by John Norstad (2002-09-11). This paper describes all the math I needed to calculate optimal portfolios, and it provides information about stock and bond returns in the U.S. 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.

I've got a rational reason to invest in bonds for the long term -- it allows me to sleep at night.

ReplyDeleteI am 61 and have stopped working and have no pension income. I have a $750k (or so) portfolio with about 34% in bonds. When the market drops like it did in January I sleep well knowing I have $250k that is in fixed income and that it is relatively safe.

CanadianRetiredGuy:

ReplyDeleteI have always maintained that money you need over the next 3 to 5 years should not be in stocks. If your $250k in fixed income is there to dip into in case of a prolonged drought in stocks, then your choice seems quite rational to me.

But, if you have more money in fixed income than you will need over the next 5 years, then I can't find a rational reason for this. Stocks go down and stocks go up. No money is made or lost unless you buy or sell.

I have several Aunts and Uncles who won't touch stocks at all because they wouldn't be able to sleep at night if they did. In a sense they are being rational about understanding their psychology. But this is sort of like being rational about one's own irrationality.

The only family member in my parents' generation I have talked to about the advantage of stocks is my mother who is doing quite nicely with her dividend income. However, she is probably more rational than I am.

Hi there Michael,

ReplyDeleteDoes the model include consideration of:

- multiple periods of time where,

- returns, standard deviations and correlations between asset classes are unstable

- returns are not fixed from period to period but vary like the market does, with multi-year sequences of ups or downs?

In his chapter 9 on Portfolio Optimization in the Asset Allocation book, Roger Gibson notes the instability of estimates of returns, of volatility(standard deviation of returns) and of correlation and the fact that small changes greatly affect the optimization results. Bonds always figure in there somewhere even when he does sensitivity analysis with the variables. The stumbling block is always in the assumptions, not the math formulae.

CanadianFinancialDIY:

ReplyDeleteI agree that the stumbling block is assumptions and not the math. I hoped to demonstrate that by showing what a radical difference it makes to change the interest rate on borrowed money. Increasing the borrowing rate by about 4% caused the optimal strategy to go from nearly 3:1 leverage with a big block of bonds to no leverage and no bonds.

For this particular analysis, I used John Norstad's data from the US from 1926 to 1994. In the past, I have used figures from other researchers over other (long) time periods, and things change, but the conclusion to avoid bonds has been a constant. However, I don't claim to have done an exhaustive survey of all data collected by all researchers.

One could repeat this analysis using, say, 80 rolling 10-year periods. Suppose that in 10 of those 80 periods, the result is that involving bonds in your asset allocation helps returns. The question then is how much did it help in those 10 periods, and how much did you give up in the other 70 periods.

I'll think about all this some more and see if I come up with anything worth posting.

Hi Michael,

ReplyDeleteLets look at the past... 2002 & 2003 the TSX was down about 13% each year. Most people (media) thought this was the end of the world. If you look at some balanced funds the return in these years was less than half the down side.

Now looking in the future, what if the bonds did not distribute income only capital gains? Would you buy? Bonds give you a different asset class, very important in down years!

regards,

Brian

Hi Brian,

ReplyDeleteIt's certainly true that holding bonds in years where stocks are down helps to cushion the blow. However, these savings are relatively small compared to the losses that come from failing to be fully invested in stocks in years where stocks perform well.

For money I won't need for at least 3 years, I'm content to invest it 100% in stocks, ignore the media, wait out poor periods for stocks, and make more money in the long run.