Risk and Return Relationships For Different Asset Allocations

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After looking at how other people and mutual fund companies choose their asset allocation, I’m a little conflicted. Both the Vanguard and T. Rowe Price mutual funds recommend holding nearly 80% in stocks at age 50. That’s pretty aggressive in my book. To see why, let’s look at some historical numbers.

Coincidentally, a commenter left me a link to a recent FundAdvice article about fine-tuning your asset allocation. I’m actually going to ignore the specific components of his portfolio and focus on the general trends instead. Let’s just say it’s well-diversified.

The article provides historical numbers (1970-2006) that compares risk versus return for portfolios ranging from 0% stocks to 100% stocks. Risk is represented by standard deviation, a measure of volatility.

Risk vs. Return For Varying Stock Percentages
Risk vs. Return

This is pretty consistent with a lot of other similar charts I’ve seen. You’ll notice that the slope of the curve decreases as you move towards holding more stocks. Accordingly, if you compare the differences between successive dots, there risk gap grows larger and the return jump decreases. In other words, you are generally getting less return for each unit of risk as you keep adding more stocks.

Here is another risk-reward chart for increasingly aggressive portfolios.

Still, this chart really doesn’t help too much either. Why not just go for the 100%? Instead of averages, let’s focus on how bad it can get over the same time period (returns not annualized):

Worst Returns For Various Portfolios

This second chart is more important than the first one, because you won’t get any of the returns listed above unless you can “stay the course” through periods such as these.

It’s really easy to say “Oh, 30% drop, no problem”, but that’s not the whole picture. Not only will stocks be dropping, but bonds may be skyrocketing. Imagine if bonds are returning 15% a year at the same time stocks are going down 15%. You will have what appears to be a way out! Personal finance magazines will be shouting “Bonds are back!” Cutting down on your stock exposure will become the “prudent” decision.

Going back to the 80% stocks at 50 years old… Can you imagine losing 35% of your portfolio in one year at 50 years old? I would freak out. This is why age matters, it’s so much easier to shrug off losses when you know you won’t need the money for another 30+ years.

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  1. I think the graph with the colored circles is a little misleading. Why? It’s on a linear scale. A, say, 2% increase in an annual rate of return makes a non-linear difference in actual investing results when you consider the effect of compounding year over year.

    For example, $10k invested for 20 years at 8% (compounded annual) will net you roughly $46.6k. If the rate was 10%, you’d net out at $67.2k. But if the rate is 12%, you net out at $96.k. The jump from 8% to 10% was roughly $20k more, and the jump from 10% to 12% was $30k more. The second 2% jump was worth 50% more than the first. Clawing out an extra percentage point can make a huge difference.

    I’d like to see a version of that graph that plots actual investment returns over a long period of time, along with standard deviation. (I definitely do want to see standard deviation – despite the above, I’m not advocating that 100% stocks is the best way to go.)

  2. I think asset allocation has to be one of the most difficult topics to understand. Everyone seems to say you should do it but I haven’t ever found anyone that says that this is how you should do it. It’s always “asset allocation will vary from person to person depending upon risk tolerance.” While I understand the importance of picking a strategy and sticking to it all this talk in the financial industry about allocation should have an end point. Some one should be able to show me a chart that says “If you are looking to invest over the next 30 years and can accept lots of risk then your optimal asset allocation would be X.” I would think that we should be able to compute these numbers fairly simply and spit out the asset allocation with the probability of highest return based upon the requested risk.

    I’m curious where you saw that T. Rowe Price and Vanguard recommend a bond allocation of 20% at age 50? I know I’ve heard T. Rowe recommend using the equation: 110-age*1.25 = % Should be invested in stocks. This would yield 75% at age 50 or 25% in bonds, not much more but different.

  3. Brian, that’s a good point. But does a linear increase in standard deviation also increase the swings nonlinearly accordingly? I need to brush up on my math.

    Jeremy – You can compute these numbers based on historical returns. That’s pretty much what the IFA link in the post above tries to do. One just has to decide how closely the future will match the past. Everyone wishes there is one correct answer, but that would require psychic abilities.

    See my previous post, where I analyze the Target Retirement funds of TRP and VG. At 15 years to retirement (ostensibly age 50), they both have 70-80% in stocks. TRP’s 2020 fund has a target of 80.25% stocks according their site.

  4. saladdin says:

    I tried to post this once but it did not take.

    Your r squared is .50 which is wayyyy low for a linear assumption. Anything under .70 or .80 means there is no positive correlation between the two variables.
    Since you are in fact trying to use this model to predict an outcome your r square value is saying there is no correlation, which means this model has NO predictive value.

    Of course I did not get my MBA at an IVY league either so take it for what it’s worth.

  5. I checked out that FundAdvice article, and I really like this quote: “And the past is a more reliable indicator of risk than of returns.”

    Going too conservative is probably less of an error than going to risky. My own portfolio is more conservative than my mind, because I didn’t know my mind when I was beginning. I’m slowly changing now it to match me.

    The best advice I’ve seen for beginning investors is to set your allocations at the conservative end of your comfort range, because until you’ve been tested in fire you don’t know your own mind. It’s easy to feel like your are not risk-averse until you’ve weathered the risky times. But to bail at the bad time of a risky portfolio is much worse than to stay the course on a portfolio that is more conservative than you.

  6. I used to deal a lot with a similar calculation (using the standard deviation of market values for particular high-risk securities) and we would see definite patterns of upswings (and downswings). Some of the more “quant”-ish people understood the stuff better (I’m just a little ol’ programmer), but I feel like these risk calculations (based on prior movement) did very little to predict real risk. It showed you what you’d just been through, but relying on them in anyway would prove dangerous (IMHO).

    Because, like you’ve shown that in 50 months you may have the opportunity to erase any bad stuff that’s happened — you don’t really know at which point during that 50 months that you jumped in. If you had made out really well in the beginning, but saw your earnings shrink down instead of evening out and going up – you would definitely have missed out on opportunities. I see the value of these calculations somewhat — maybe as a component of a more fortified calcuation (many more factors than past performance).

  7. In “4 Easy Steps to Successful Investing”, by Jonathan D. Pond states to determine the percentage of stock to hold use the following rule-of-thumb formulas:

    100 – Age = Conservative Investor
    110 – Age = Moderate Investor
    120 – Age = Aggressive Investor

    He further states that there is no one formula that would work for everyone. For instance if you are nearing retirement and will be able to live comfortably on social security and a pension, then you can probably afford to have more equities in your portffolio.

    To me, that means, if you live within your means and can save at a steady rate earlier in your life and for longer periods of time, you can afford to have more of your investments in equities for a longer period of time.

  8. This may be a dumb question…but what is the advantage to placing funds in bonds as opposed to high yield savings accounts like emigrantdirect?

  9. MossySF says:

    The fact that you can get interest rates on savings accounts matching/exceeding bond yields is a FLUKE of the current fiscal/credit insanity. Look back at the rates for ING back in ’03 — 2% APY. During the same time, Vanguard’s bond funds had yields of 4%-6% depending on the maturity.

  10. Just to make sure I understand. Is the percentage of loss shown over the worst month, twelve-month, etc. for only the stock portion of your portfolio, or over the entire portfolio? Example, for a 30% stock portfolio, is the chart saying that the stocks that make up 30% of my holding are down 9.8%, or would the calculation include the entire portfolio being down 9.8%.?

  11. saladdin – I assume you are talking about the first graph in the previous post. You are certainly correct in that any research study that would extract a linear model from data that scattered would be laughed out of the room. But we weren’t trying to get a model out of the data, we were just trying to see how it compared to something already existing in very general terms.

    Don – I think that’s my main point here. It is better to be slightly more conservative than needed, rather than to too risky. I think I’m more worried about people closer to retirement than farther away. I’m almost detached to my retirement savings, it has so long to go. Hopefully that means we are less prone to bailing out.

    Dan – I think it also depends, do you want to leave an inheritance? Otherwise, you could party 🙂

    tyler – Historically, high-yield savings accounts and money market mutual funds have returned essentially nothing after inflation. Bonds of a certain term have faired better, and also serve to be a better diversifier to stocks. That is, when stocks go up, bonds then to go down, and vice versa. Thus bonds would be a better long-term strategy. This is how I understand it.

    Right now, the inverted or almost-inverted yield curve is a bit wonky. Some people say staying in cash right now is fine. I’m not sure how easily one can time going back and forth between cash and bonds, but I don’t plan on bothering.

    S – Entire portfolio.

  12. At 28 years old, I’m perplexed as to why I should have ANY of my retirement funds in bonds. Even if I retire at 60, that’s over 30 years away. Is there any 30 year period in which stocks do not outperform bonds? The 120-age/110-age, etc formulas might be worthwhile as I get older, but for now, I think 100% stock is the way to go.

  13. From 1965 through 1974, U.S. stock prices had an annualized return of only 1.25 percent. In those same 10 years, one-month certificates of deposit returned 6.5 percent.

    From 1984 through 2002, a bond portfolio made up of 3 equal parts of Short-Term Investment Grade, GNMA and Long-Term Corporate Grade bonds produced an annualized return of 9.2 percent for buy-and-hold investors.

    In the Four Pillars of Investing, Dr. William Bernstein recommends holding some cash in your portfolio (5-10%). In bear markets, the cash will come in handy on buying sprees.

    It’s in these shorter periods, with periodic portfolio rebalancing that you can take advantage of a tremendous buying opportunity and add wealth to your portfolio. Having a portfolio of 100% equities will make it harder to go on buying sprees.

    At 28, holding a portfolio of 5%-10% bonds (50/50 split between Short Term Investment Grade & Total Bond market) and 5%-10% cash can be helpful.

  14. Steve the K says:

    It is Wall Street that equates volitility with “risk”. But there are different definitons of “risk”, e.g., chance of losing everything, chance of losing principle, chance of losing buying power (inflation).

    Ron Muhlenkamp talks about “risk” [1]. The wavy blue line is more volitile than the top red line, hence it has higher risk Wall Street will also tell you that the wavy blue line is higher risk than the middle red line and higher risk than the lower red line. You can get the bottom and middle red lines, but the top red line does not exist. You can, however, get the wavy blue line.

    Volitility is also a function of sample rate. Over the past 50 years, the S&P 500 has had 13 down years. [2] If you take a 3-year running average, it drops to 3 years.

    My question about the chart in the original article is, is the “worst 50 months” the worst fifty CONTIGUOUS months or the worst SELECT (not necessarily contiguous) months?

    Note: I am an investor in the Muhlenkamp Fund.

    [1] http://www.muhlenkamp.com/show/basics/slide18.html
    [2] http://www.muhlenkamp.com/show/basics/slide19.html

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