How should an asset allocation change over time? Most folks (financial professionals included) believe that the longer your time horizon the more risk you can take. That, as stated, is clearly wrong. Let me explain by way of an example. Assume an individual is 35 years old and inherits $1,000,000. He or she will not save any additional funds and at age 65 will annuitize for retirement whatever that sum has grown to. We will ignore taxes or other complications. Now, suppose that over the next 30 years, one year will have a positive 100% return (i.e. the portfolio doubles), one year will have a negative 50% return (i.e. the portfolio halves), and the remaining 28 years will each have a return of 6%. To maximize the ending value, what sequence of those returns would be best?
I have been asking that question of financial professionals in classes for about a decade now (I don’t remember specifically when I started, but it’s been a while). Almost never do I get the correct answer. Some just have no idea and guess, but most say you want the bad return first (when the portfolio is smallest), the 28 returns of 6% next, and the best return at the end (when the portfolio is largest). I then chide them (with a smile) for failing third grade math. It’s in the third grade that I think most students learn the commutive properties of addition and multiplication. Our problem may be stated mathematically as:
($1,000,000) x (2) x (0.5) x (1.06^28) = $5,111,687
The parenthesis are just there for readability. The point is that the answer doesn’t change if you rearrange the order of the terms (the items in parenthesis)! A x B x C = C x B x A! It also doesn’t matter what the returns are – any 30 returns will give the same ending value as the same 30 returns that simply occurred in a different order.
In other words, if our investor can’t afford the risk of a 50% loss the year before retirement, he or she also cannot logically afford to take such a risk at age 35 either – it’s the same risk! In the absence of cash flows, the time horizon is utterly irrelevant to the asset allocation decision.
Nonetheless, it seems intuitively correct to change the asset allocation over time to a more conservative one. And I think that is right, but it is for a different reason than commonly assumed. Few people have a lump sum as used in the example above. They are actually converting their human capital to financial capital over time. So we don’t have two buckets (stocks and bonds) but three (stocks, bonds, and human capital). A young person’s human capital (the present value of future wages) will significantly dwarf their financial capital in the early years. Assume for simplicity that human capital was equivalent to bonds (more on this below). Further assume that to reduce risk we want half our assets to be kept safe. But we don’t have human capital in cash and can’t implement this allocation in practice. Rationally, a 35 year old should borrow against future earnings to reallocate human capital to stocks. There are significant constraints to doing so however. What we can do is “borrow” by reducing the bond position much lower than we would if there were no human capital in play. Selling bonds is equivalent to borrowing. We can take the proceeds and invest in stocks to improve our allocation. So, because of borrowing constraints our hypothetical investor should perhaps be 100% stocks in their financial portfolio at young ages and this is not risky because of the enormous allocation to human capital that still exists. (Of course it’s still prudent in most cases to have an emergency fund – or perhaps a HELOC, a wealthy parent, or something similar.)
This assumes that human capital is bond-like. It probably depends on the career, but research indicates that human capital is generally more bond-like than stock-like. Traditional stock brokers and big-ticket luxury goods workers are correlated in their wages with stocks somewhat (but perhaps not ultra-luxury goods which may be uncorrelated or small dollar luxuries which may be negatively correlated), securities attorneys (who litigate) are negatively correlated with a lag (and I think high-quality advisors are too) but most folks are relatively uncorrelated in the short run (though in extreme cases such as the great depression equity markets and human capital may suddenly become highly correlated). In the long run if the economy grows 4% per year both pay and stocks will do much better than if the economy grows 2% per year. In addition, things like Social Security are more sustainable if the economy has been growing at a faster rate. So there may be very valid reasons not to lever up to extreme levels to buy stocks even when young, but overweighting stocks seems very prudent.
In short, time horizon doesn’t matter to your asset allocation, but your human capital certainly does.