Efficient Asset Allocation: Stocks or Bonds?

Tuesday, December 21 2004 @ 09:03 PM EST

Contributed by: martingale

One tough nut in investing is the question of asset allocation: how much money should you invest in short-term bonds? How much in stocks? There's much debate over this point, but I will do my best to give you some sound advice. You do need to heed this warning, though: there are no guarantees: For every possible investment strategy there is a future in which it was the wrong choice. First, we will cover the basics and work out the absolute minimum amount you should have in bonds. What's left can go into stocks. Then we will turn our attention to the efficient frontier: the interesting, counter-intuitive property of the market that it is always better to have a mix of stocks and bonds than to have 100% of just one or the other.

Any discussion of asset allocation must necessarily start with an analysis of your own financial situation. Your asset allocation plan invariably does depend on how much risk you can tolerate. In assessing your risk tolerance there are two key quesitons you need to answer:

The first question looks objectively at whether you can actually afford to take risks. It is foolhardy to risk money that you absolutely need. The second question is more subjective: Even if you can afford it, it's silly to take risks you don't have the stomach for--if the risks would cause you to lose sleep, or worse, panic and sell out all your investments at just the wrong moment, then you'd have been better off taking less of a risk.

Often planners lump all your income together and give you a draw rate, and only one "failure" condition is contemplated--the prospect that you will wind up with less than your stated retirement needs. In reality for most people there is a hard minimum amount of money that you absolutely must have, and everything beyond that is luxury. Most people can afford to take risks with the luxury portion of their retirement savings--but the bare minimum must be protected.

What do I mean by "bonds" here?

Let's clear up one misconception straight away: When someone tells you that you should invest in bonds because they are safe they are telling you to invest in short-term bonds. That means high quality corporate, municipal, and government bonds with a term of less than five years. Longer term bonds are not risk free: they are exposed to considerable interest-rate risk, and can easily lose a substantial amount of value in a day. Long bonds have a place only in sophisticated portfolios as hedges against certain kinds of risk, and if you don't understand what I'm talking about then you should not be holding any long-term bonds.

In all that follows when I advise you to buy bonds I mean high quality bonds that have a term of 5 years or less.

The Risk of Eating Alpo

In this section we will cover the personal form of risk, as opposed to the stock market sort. By this I mean the risk that you will wind up eating Alpo in your old age.

Take a hard look at your life and figure out what is the minimum amount of money you could survive on: I mean, no luxuries, no frills, no tropical vacations, nothing but the most spartan lifestyle: what does it cost you to eat, to buy simple clothes, and pay for a modest apartment. Put a number on it: how much will you need every year, at an absolute minimum? You need to ensure that even in the worst case outcome your financial plan will provide you with this minimum amount. We will use this number to work out, roughly, the minimum amount of your portfolio that must be invested in safe investments like short-term bonds. Chancing this money on riskier investments would be foolhardy. You can risk other money on a luxurious life but this basic minimum amount must be protected.

Write down this minimum monthly income on the back of the nearest envelope. Add a third for taxes (a 25% tax rate). Subtract your expected CPP and other pension benefits. Multiply this monthly amount by 400 to come up with the total capital you will require (12 months / 0.03 draw) . Subtract the equity you will have in your home when you retire (do not expect any gains, use today's market price). This is how much you will need to save up through short-term bonds. This very conservative number assumes you can draw down just 3% of your savings per year. Many planners think you can draw down much more, but we're talking life-support here, so let's be conservative--you might face some unexpected costs, and if we get this bit wrong you'll be eating Alpo.

For example, let's say you need a minimum $1800 a month to live, that's $2400 before tax, of which you expect $800 will come from pension plans, so you multiply $1600 * 400 to rough guess that you need $640k in capital to support your basic needs. You will have paid off your $250k home by the time you retire, so you realize you need to save another $390k. This is back of the envelope stuff, but it'll do for estimating a reasonable minimum stock/bond allocation.

The mathematically tricky bit is working out how much money that is today--I have provided a table with some common values for you, but you may need the help of a spreadsheet or financial calculator with an amortization function to figure out your own particular situation.

How much $1 dollars today will be worth What a $1 invested each and every year grows to
$1 in 10 years$1.410 $1/y in 10 years$11.731
$1 in 15 years$1.675 $1/y in 15 years$19.295
$1 in 20 years$1.989 $1/y in 20 years$28.279
$1 in 25 years$2.363 $1/y in 25 years$38.950
$1 in 30 years$2.806 $1/y in 30 years$51.623

I've assumed a 3.5% real return on bonds, meaning, the return you get after inflation. In this and all other calculations we will always deal with inflation by using the real return. So if interest rates are 5.5% and inflation is 2% we will assume a real return of 3.5%. It's easier this way--we can think of future costs as if they were paid for at today's prices. Note: We are using extremely conservative numbers in this calculation because we are looking at only the most conservative part of your portfolio. The yields on equities are much higher, but they are risky. You must cover your absolute minimum cost of living with conservative investments.

Look in the table for the number of years until you retire and multiply your current bond holdings by the value in the second column. Subtract that amount from the minimum savings you will require. Divide whatever is left by the value in the fourth column--this is the absolute minimum amount of money, per year, that you must invest conservatively every year from now on. In our example, if you plan to retire in 20 years, and you have $40k invested conservatively, that will be worth about $80k. You will need another $310k to reach your target of $390k, which will require investing a further $13,800 per year or roughly $1150 a month.

That tells you that, going forward, you need to allocate a minimum of $1150 per month to conservative investments in order to ensure that you will be able to cover your bare minimum living expenses. For many people the mathematics of this are grim, and meeting even this minimum requirement is about all they can afford to do. If you fall into that case consider whether the minimum you can live on might be less. Alternately, if you can tolerate leaving nothing to your kids you could multiply by 300 instead of 400 in the above calculation and look into buying a life annuity from an insurance company when you retire instead of holding bonds. A life annuity will yield more income per month, and it's guaranteed for your whole life, but at a steep cost: the insurance company keeps everything when you die.

If that's all you can afford to invest then you're almost done. Nearly all this money should be invested in bonds: skip down to the last section, titled Mixing it up On the Efficient Frontier, to learn that you should still put just a little in stocks.

Risking a Life of Luxury

If you have some extra money to invest you can consider putting it into equities. Since this money is above and beyond your basic needs any gain or loss here will impact the luxuriousness of your retirement. You will earn a much higher return than if you invest in short-term bonds, but you get that return by taking risks. How much you should invest in equities depends on your stomach for risk.

Few people know how they will react when a large chunk of money they used to own starts to vanish in a market meltdown. When the stock market bubble burst in 2000 many bailed out in disgust. That panic reaction meant those investors, who bought high, sold low. Everyone who bailed believed they were risk tolerant back when they placed their "buy" orders: It is one thing to take on a risk, it is quite another thing to experience loss. Risk tolerance means being able to stand around doing nothing while your money disapears and everyone you know says you're an idiot for standing pat. Worse, you're pouring more good money in after bad. The market pays you to take risks by providing higher expected returns on risky investments--those who invested at the darkest hour were well rewarded on the rebound. But taking that chance means being able to stand the reality of losing money.

Reflect on your life. When you lose money do you think nothing of it? Or do you fret and worry? Come up with a number in answer to this question:

Multiply that number by two. That is the most that you should ever invest in the stock market. If the standard deviation on equities continues to be what it has been then once every five years equity investors will lose 20% of their money, and once every 30 or 40 years they will lose 60%. Usually, it bounces back, but you will see the value of your portfolio fall, and you need to know how you will react: Will you see it as an opportunity to buy in at the bottom? Or will you panic and sell? Your retirement plan likely spans decades so this is something you will probabably experience at least once in your life.

That being said the rewards are huge. Historically, the return on bonds has been a miserable 3-4%. The return on equities has been three times that much. We cannot expect the future equity returns to look like historic returns, but we certainly can expect that an investor who takes on a higher degree of risk will still deserve a higher return.

Note that there are two kinds of risk: the overall risk of investing in stocks ("systemic risk"), and the specific risks faced by an individual company or industry ("non-systemic risk"). You only get paid to take on the general sort of risk because anyone can eliminate the specific risks by diversifying: If you own enough different kinds of equities it won't matter if one or two industries tank, so long as the others do well. The real risk you face is that the market as a whole will crash, or "underperform". We will talk in a different article about exactly how you should diversify yourself in equities.

Mixing it Up on the Efficient Frontier

Many investors make the mistake of thinking that the least risky portfolio is one containing just cash and short-term bonds; or that the most aggressive portfolio is one containing only equities. Somewhat surprisingly, that is false. The safest portfolio contains a mix of stocks and bonds, as does the most aggressive. For any portfolio containing all bonds there is a less risky portfolio with a better return that contains some stocks. This is counter-intuitive because in and of themselves bonds are safer than stocks--but I will do my best to explain it.

The key here is that you will rebalance your portfolio once a year. You will start out the year with, say, 90% bonds and 10% stocks. By the end of the year as prices shift you may find you now have 95% bonds, or 85% bonds. If that happens, then at the end of the year, you will sell some bonds or stocks as necessary to get back to your 90-10 split (or whatever ratio you have chosen).

It will happen fairly often that losses in the bond market will be mitigated by stocks having had a good year; or that losses in the stock market are compensated for by a good year in bonds. It is this mitigating effect, one asset making up for losses in the other, that makes the portfolio less risky. When you rebalance you will be selling an asset that has risen to buy one that has fallen. Often enough this will be a good move. (For the mathematically minded, what is important here is that the returns on bonds and stocks are somwhat independent of one another: they are correlated, but the correlation is well below one).

Let's consider a few examples: Below I've created a table comparing an all-bond portfolio to one with 10% stocks, under a few different outcomes:

$1000 Bond
$0 Stocks
$900 Bonds
$100 Stock
Stocks +15%
Bonds +5%
+$50 +$60
Stocks -5%
Bonds +5%
+$50 +$40
Stocks +15%
Bonds +0%
Nil +$15
Stocks -5%
Bonds +0%
Nil -$5
Average Real Return 2.47% 4.52%
Risk (stdev) 2.88% 2.84%

So the mixed portfolio had a much higher return for about the same risk, or even slightly less risk. Note that these returns are invented: I've imagined stocks swing between +15% to -5% and that bonds either return 5% or break even. This is typical of historic behavior but who knows what the future will hold. No matter what values are chosen, though, the principle will remain true: the mixed portfolio will have a higher return, for roughly the same risk. A portfolio of 5% stocks would have been much safer than an all bond portfolio, rather than the same risk.

Sharp-eyed mathematically inclined readers have noticed a problem with my example: It assumes that there is no correlation at all between bond and stock returns. In reality there is a correlation, but it is much less than one: bonds and stocks tend to move in the same direction, but not always. So the actual advantage of mixing up your assets like this is slightly less than in my simplified, contrived example. Nevertheless, the principle holds.

At the other extreme, for an investor who wants the absolute highest return regardless of the risks, there is still a big advantage in holding a mix. The return of a portfolio containing all stocks is only slightly higher than the return on one that contains 20% bonds; meanwhile the risk is much, much higher for the all-stock portfolio. It is silly to take on a lot of extra risk for only a slight extra reward--there is a diminishing return to increasing the equity portion of your portfolio much beyond 75 or 80%.

The efficient frontier is a mathematical/investment term for a portfolio which has the maximum return possible for a given level of risk, and that's where you want to be. Unfortunately the correlations and standard deviations of different assets, like "stocks" and "bonds" change constantly--so there is no way to know exactly where this efficient frontier is. You can, however, make some effective guesses: It is highly unlikely that the most efficient portfolio is all stocks or all bonds. It is highly likely that it will be some mixture.


If you are a conservative investor seeking the safest portfolio you can hold you should still have somewhere between 5-10% of your assets in stocks. If you are an aggressive investor, then once you have met your minimum living standards, you can invest in equities up to your risk tolerance--but you should still have, as a minimum, at least 20% of your portfolio in short-term bonds.