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Calculator for Backtesting a Portfolio or Asset Allocation (Also Monte Carlo Simulations)

A reader writes in, asking:

“Is there a website or calculator that you recommend for showing the historical results of a portfolio? Something where I can enter an asset allocation and the calculator will tell me what the return would have been and how risky.”

Yes, absolutely. PortfolioVisualizer.com is an excellent tool for this sort of thing. From the homepage, select the link for “backtest asset allocation” if you want to choose from inputs such as “US large cap,” or click the link for “backtest portfolio” if you would prefer to provide the ticker symbols of specific mutual funds.

The calculator lets you adjust your modeling for various rebalancing options. For example, you can assume the portfolio is rebalanced monthly, rebalanced annually, never rebalanced, or rebalanced using “rebalancing bands” (e.g., rebalanced whenever the allocation is off-target by 10%).

And it lets you make assumptions about ongoing contributions to, or spending from, the portfolio. You can make adjustments such as whether the spending is a fixed percentage or a fixed dollar amount. (And if it’s a fixed dollar amount, should it be inflation-adjusted over time?)

After you provide all of your inputs, the calculator tells you the historical return, standard deviation, best/worst years, maximum drawdown, and other various results.

PortfolioVisualizer also has the option to run Monte Carlo simulations. (Select the link for such from the homepage.) On the Monte Carlo simulation page, you can have it use historical data, or you can select other options for the return assumptions (e.g., “parameterized returns,” which lets you input expected return and standard deviation for yourself).

The PortfolioVisualizer website also has a ton of other calculators that I’ve never even used. In short, it’s an incredible resource. And it’s free. (Though there’s also a paid version that gives you some additional capabilities, such as saving results, exporting to spreadsheets, etc.)

Of course, when backtesting, be sure to remember the limitations of relying on historical data. Just because a portfolio provided a particular return in the past doesn’t mean it will do so in the future. And the same goes for all of the other outputs (e.g., how risky an allocation would be, or whether it would have satisfied a particular spending rate in the past).

And ditto for the Monte Carlo simulations. They can be useful, but remember that we don’t actually know what the future distribution of returns will look like for any asset class. If a set of Monte Carlo simulations shows, for example, that a particular portfolio has a 92% chance of satisfying a given spending rate over a given length of time, we don’t actually know that the portfolio has a 92% chance of satisfying that spending rate over that length of time. Rather, what we know is that, given the assumptions that you used, the portfolio had a 92% chance of success.

International Allocation: Maximum and Minimum

What percentage of the stock portion of your portfolio should be invested internationally? Vanguard’s website (in a section only accessible if you’re logged in) contains this statement:

“Investing up to 20% of your stock portfolio in international stocks can help you diversify. Between 20% and 40%, your diversification improves, but at a lower rate. And because of the risks of international investing, an upper limit of 40% is wise.”

20-40%. That’s more or less in keeping with conventional wisdom.

But conventional wisdom seems to gloss over something here: Having 80% of your portfolio (more than 80% if we assume that the entire bond portion is invested in U.S. bonds) invested in one country is not diversified–especially for anybody whose income is largely dependent upon the U.S. economy.

Past and Future

I assume Vanguard’s statement is based on an analysis of historical returns. I can only guess which exact period(s) they’re looking at, but surely it’s limited to the 20th century plus the first decade of this century–a period during which the United States went from being a young upstart nation to being the world’s largest economic superpower.

It’s hardly a surprise that based on an analysis of that period, a U.S.-heavy portfolio looks pretty darned good. What I’m not so sure we can expect is for the next 10, 20, 30, or 60 years to look the same.

Starting Point: Market-Weighted Portfolio

To me, it seems that the starting point for discussion should be a market-weighted portfolio. At the moment, such a portfolio would be invested approximately 60% in the U.S. and 40% internationally.

From there, you can make adjustments to cater to your specific needs. For example, if you’re in (or close to) retirement, it could makes sense to decrease your international allocation for two reasons:

  • First, you’re going to be spending down your investments soon, which means that it would be good to minimize currency risk (the risk caused by fluctuations in exchange rates that comes with owning non-U.S. investments).
  • Second, you have fewer years remaining in the workforce, meaning that you’re less dependent upon the U.S. economy that somebody who is, say, 25 or 30.

Avoiding the “Growth Trap”

What I’d caution against, however, is falling into the growth trap–overweighting emerging markets (China or India, for instance) simply because you know they’re going to grow at a faster rate than the U.S. over the next couple decades.

When it’s obvious that a country’s economy will be growing quickly, that growth should already be reflected in the price of their stocks. To earn above-market returns, you need to invest not in countries (or companies) that grow quickly, but in countries (or companies) that grow more quickly than expected.

If you’re going to invest more of your portfolio in non-U.S. investments than conventional wisdom would suggest, do it with the goal of diversification, not with the goal of earning superstar returns.

How Much Cash Should a Retirement Savings Portfolio Include?

A reader writes in, asking:

“What do you think is an appropriate level of cash allocation in a portfolio for retirement savings?”

Let me begin with my standard disclaimer for any asset allocation question: there’s a broad range of what is reasonable. There is no one perfect allocation, and it’s a waste of time to try to find such.

For any particular investor, there’s an approximate overall level of risk that is appropriate, and there are countless different ways to get to that level of risk. So, for example, if you like to use cash instead of bonds because doing so allows you to feel comfortable with a slightly higher stock allocation, that’s perfectly reasonable.

But, in most cases, a retirement portfolio will not require a cash allocation at all.

As for our household (still in the accumulation stage), our retirement portfolio has no intentional cash allocation. It’s all stocks or bonds. (More specifically, it’s 100% Vanguard LifeStrategy Growth Fund and has been for ~10 years.)

That said, we do keep a few months of expenses in checking accounts. In part, that’s because my own income has a high degree of variation from one month to the next. That’s just the nature of self-employment. If we were both paid a predictable monthly salary, we would probably keep a smaller amount in checking accounts.

Similarly, if we were retired and our Social Security/pension/annuity income were sufficient to pay the bills, I’d be comfortable with a very small amount in checking. Assets from investment accounts can be tapped pretty quickly. Even for an unexpected large expense, you can use a credit card to pay the expense, then liquidate some assets from investment accounts to be able to pay off the credit card promptly (i.e., before paying any interest).

As far as cash as an asset class, it does what you would expect it to do: it reduces the overall volatility of the portfolio, but it earns almost no return, even before inflation.

Some people hope to use cash holdings to actually improve returns by deploying it at opportune times, but that’s harder than it might appear. For instance, by January of 2009, the market had spent the last several months moving dramatically downward. So it was clearly a better time to buy than it was several months ago. But was this the bottom? Or would it be better to continue to wait? (If you wait, it might turn out that this was the bottom, and you end up having to buy at a higher price.)

I certainly had no idea at the time. I never have any idea where the market is heading next, so I have no interest in holding cash just to hope to take advantage of such opportunities.

And for all of the years in which the stock market doesn’t provide any crash-fueled, obvious buying opportunity, the money that you have sitting in cash is just missing out on returns.

For instance, over the last 10 years, Vanguard Short-Term Treasury Index Fund (which we can use as a stand-in for cash) went up in value by about 12%. By contrast,

  • Vanguard Total Bond Market Index Fund has increased in value by about 39%, and
  • Vanguard Intermediate-Term Treasury Index Fund increased in value by about 30%.

Depending on which comparison fund we’re looking at, that’s a cumulative 18-27% return shortfall by having the money sit in cash. That’s not massive, but it’s not nothing. And it’s not as if a total bond fund or intermediate-term Treasury fund is any sort of terrifying roller coaster ride.

So, again, cash is a perfectly reasonable thing to include in almost any asset allocation, because it’s one tool that you can use to adjust the portfolio’s overall risk level to where you want it. But it’s uncommon for a portfolio to need any cash allocation at all.

There is one specific case in which I do think cash can play a critical role. If you’re retired and you’re temporarily spending from your portfolio at a high rate until Social Security (or a pension) kicks in, it’s important to use something very safe like cash or CDs for satisfying that extra-high level of spending, because, for that money, you can’t afford to take on much risk at all.

Asset Allocation and Risk Tolerance

The following is an adapted excerpt from my book Investing Made Simple: Investing in Index Funds Explained in 100 Pages or Less.

When putting together a portfolio, the first thing to decide is your desired asset allocation. That is, how much of your portfolio should be invested in each asset class (e.g., U.S. stocks, international stocks, and bonds)?

Your tolerance for risk is the most important factor in determining an appropriate asset allocation. The primary factors determining your risk tolerance are:

  1. Your economic/financial ability to tolerate risk (i.e., how much risk you can afford), and
  2. Your emotional/psychological ability to tolerate risk.

Your economic ability to handle risk is significantly impacted by the degree of flexibility you have with regard to your financial goals.

Financial Flexibility

Example 1: Jason is a construction worker. He’s 57, and each day he is becoming increasingly aware that his body is unlikely to be able to continue in his line of work for more than two or three more years. Between his Social Security and savings, Jason is pretty sure that his basic expenses will be covered — but only barely. Because Jason can neither delay his retirement nor reduce his expenses, Jason has a low ability to take risk.

Example 2: Debbie is 54. She hopes to retire at 62 with enough savings to provide for $80,000 of annual spending. Debbie likes her work though, so she wouldn’t terribly mind having to work until her late 60s. And $80,000 is just a goal. She knows she could get by just fine with about 70% of that. Because Debbie’s goals are flexible, she has a greater ability to take risk.

Comfort with Volatility

Your risk tolerance is also affected by your comfort level with volatility. One way to estimate this comfort level is to ask yourself, “How far could my portfolio fall before I started losing sleep, feeling stressed, or wanting to sell everything and move to cash?”

When answering this question, be sure to answer both as a percentage and as a dollar value — otherwise you may come to inaccurate conclusions. For example, you may remember that at age 25 you experienced a 40% loss and handled it just fine. But if you’re 45 now, and your portfolio is 10-times the size that it was at age 25, a 40% loss could be an entirely different experience.

When assessing your risk tolerance, it’s generally wise to guess conservatively. If you end up with a portfolio that’s slightly too conservative for your tastes, you’ll only be missing out on a relatively small incremental return.

In contrast, if you end up with a portfolio that’s too aggressive, you might end up panicking during periods of high volatility. Even one instance of getting out of the market after a sharp decline can be more than enough to eliminate the extra return you were hoping to earn from having a stock-heavy allocation.

Stocks vs. Bonds

Once you have an idea of your risk tolerance level, it’s time to move on to the first (and most important) part of the asset allocation decision: your stock/bond allocation.

One rule of thumb that serves as a reasonable starting point for analysis is to consider limiting your stock allocation to the maximum tolerable loss that you determined above, times two. Or, said differently, assume that your stocks can lose 50% of their value at any time.

The most important thing to remember with asset allocation guidelines, however, is that they’re just that: guidelines. For example, with regard to this particular rule of thumb, it’s important to understand that a loss greater than 50% certainly could occur, despite the fact that such declines are historically uncommon. This is especially true if your stock holdings are not well diversified or if your non-stock holdings are high-risk such that they could decline significantly in value at the same time that your stocks do.

U.S. Stocks vs. International Stocks

As you might imagine, the U.S. stock market isn’t the best performing market in the world every single year. In fact, it’s often not in the top 10.

The difficulty in international investing — as with picking stocks or actively managed mutual funds — is that it’s nearly impossible to know ahead of time which countries are going to have the best market performance over a given time period. The solution? Own all (or at least many) of them.

The primary goal of investing a portion of your portfolio internationally should not be to increase returns, as there is no guarantee that international markets will outperform our own. Rather, the primary goal is to increase the diversification of your portfolio, thereby reducing your risk.

In total, the U.S. stock market makes up roughly half of the value of all of the publicly traded stocks in the world. However, for two reasons, most investment professionals recommend allocating more than 50% of the stock portion of your portfolio to domestic equities. First, international funds generally have somewhat higher expense ratios than domestic funds. Second, investing internationally introduces an additional type of risk into your portfolio: currency risk.

Currency risk is the risk that your return from investing in international stocks will be reduced as a result of the U.S. dollar increasing in value relative to the value of the currencies of the countries in which you have invested.

EXAMPLE: A portion of your portfolio is invested in Japanese stocks, and over the next year it earns an annual return of 8%. However, over that same period, the value of the yen relative to the dollar decreases by 3%. Your annual return (as measured in dollars) would only be roughly 5%.

So how much of your portfolio should be invested internationally? There’s a great deal of debate on this issue, with investment professionals recommending a very wide range of international allocations.

Without knowing how the U.S. market will perform in comparison to markets abroad, there’s simply no way to know what the “best” allocation will be. In my own opinion, there’s a pretty broad range that’s reasonable. Allocating anywhere from 20% to 40% of the stock portion of your portfolio to international index funds would be reasonable for most investors—with the general idea being to give international stocks a somewhat smaller weighting than their (roughly) 50% market weight (due to their higher costs and currency risk), while still making sure that the international allocation is of sufficient size for it to offer a meaningful diversification benefit.

Rebalancing

No matter how perfectly you craft your portfolio, there’s little doubt that in not too terribly long, your asset allocation will be out of whack. The stock market will have either shot upward, thereby causing your stock allocation to be higher than intended, or it will have experienced a downturn, causing your stock allocation to be lower than intended.

Rebalancing is the act of adjusting your holdings to bring them back in line with your ideal asset allocation. A periodic rebalancing program helps keep the risk level of your portfolio in line with your goals.

How often should an investor rebalance? That’s a tricky question. Some people advocate in favor of rebalancing once your portfolio is off balance by a certain amount (such as your stock allocation being either 10% higher or 10% lower than intended). Others argue that rebalancing should be done at regular intervals (annually on your birthday for instance) regardless of how off-balance your portfolio becomes in the interim.

The best-performing rebalancing strategy varies from period to period, and it’s no easy task to predict which one will do best over the course of your investing career. Rather than spending a great deal of time and effort thinking about it, my suggestion is simply to pick one method and resolve to stick with it.

It’s worth noting that rebalancing can be quite difficult emotionally/psychologically. It can feel as if you’re selling your “good investments” to put money into your “bad investments.” The key is to remember that just because something has performed well (or poorly) recently doesn’t mean that it will continue to do so in the immediate future.

Simple Summary

  • Your tolerance for risk should be the primary determinant of your stock/bond allocation. Your risk tolerance is determined by how much risk you can afford and how much risk you can tolerate psychologically.
  • Generally speaking, it’s better to have an asset allocation that’s too conservative than an asset allocation that’s too aggressive.
  • For the sake of additional diversification, most investment professionals recommend investing somewhere from 20% to 40% of your stock holdings internationally.
  • Rebalancing is the act of bringing your portfolio back to its targeted asset allocation (and, therefore, its targeted risk level).

Overweighting REITs: Why Don’t More Experts Recommend It?

A reader writes in, asking:

“My husband & I are on a pension & SS. We have been retired for 17 years but inflation has been fairly low. However we can see our medical bills & insurance going up just about every year. I learned about REITS from reading on the internet. You mention them in your book but almost as an afterthought. With interest rates so low & getting lower why wouldn’t you want more of your money in REITS if the majority of your income is guaranteed?

Why do REITS seem to be a secret? Money columnist in the paper never mention them.”

Because REITs are stocks, they are already included (at their market weight) in a “total stock market” sort of index fund. So the primary question with REITs — as with any subcategory of stocks (e.g., value stocks, small-cap stocks, or any other industry-specific category of stocks) — is whether overweighting them in a portfolio improves the portfolio’s performance.

That’s a trickier question than it might appear at first, because performance can be measured in a number of different ways and because results vary considerably depending on what period we look at. But in most cases, the answer seems to be “no, it doesn’t particularly improve the portfolio to overweight REITs.”

For instance, here’s a paper from Vanguard that looked at whether adding a tilt to REITs (or commodities) would improve their target-date funds (or target-date funds in general). Here’s what they found:

“The results suggest that when adding commodities or a REIT overweight relative to the Vanguard glide path, the improvements are minimal at best. Of the outcomes generated by the addition of REITs, for example, those in the 5th percentile see a 0.20 increase in the wealth multiple, while those in the 95th percentile see a 2.77 decrease in it.” [Mike’s note: by “wealth multiple” here, they are referring to wealth at age 65, as a multiple of the hypothetical person’s ending salary.]

Or later in the paper:

“Our analysis suggests that even if alternatives can be used at a low cost and with limited administrative complexity (and participant confusion), these strategies are likely to deliver modest benefits at best. Our conclusions are consistent with earlier Vanguard research, which finds that any improvement in participant outcomes produced by changes in sub-asset class allocation is likely to be small compared with what can be achieved through other strategies such as reducing investment costs, increasing savings amounts, adjusting retirement age, and managing the desired replacement ratio.”

Or, here’s a relevant paper from Jared Kizer of Buckingham Strategic Wealth and Sean Grover of Georgetown University. The paper looks at a broad set of questions about REITs, but here is what the authors had to say on the topic of adding a specific allocation to REITs in a stock/bond portfolio:

“Utilizing tests of mean-variance spanning, we also examine the diversification properties of REITs on a statistically inferred basis. These tests suggest that REITs do not reliably improve the mean-variance frontier when added to a benchmark portfolio of traditional stocks and bonds.”

(If you’re interested, you can also find a somewhat easier-to-digest summary of that research in an article from Larry Swedroe here.)

The point isn’t that overweighting REITs makes a portfolio worse. But it doesn’t seem to make it clearly-better either.

An important aspect of this conversation is that, while REITs provide a higher level of income than most other stocks, income from investments is not, in itself, a useful goal. Rather, it’s total return that matters, because capital appreciation can be used to fund living expenses just as well as income can. For instance, in a given year, if a given mutual fund provides an 8% total return, it does not matter whether the return is 8% from income and 0% from capital appreciation, 8% capital appreciation and no income, or any other combination in between.

An important exception is that if we’re talking about a taxable account (as opposed to retirement accounts such as IRAs or 401(k) accounts), income is actually detrimental relative to capital appreciation, because it results in an immediate tax cost rather than a deferred tax cost. And as a result, it can even make sense to underweight REITs in taxable accounts.

Simplifying a Retirement Bucket Portfolio

A reader writes in, asking:

If you were developing different “buckets” for a portfolio in retirement, what funds would you use for each bucket?

For our immediate 1-3 years, I have assigned that duty to the Vanguard Ultra Short Bond Fund. It has a duration of one year, and does not have any government bonds.

Do you think that fund is too risky – both in terms of duration and in terms of risk? Should we have at least one year in money markets?

For our 3-6 year buckets, we use a variety of short term bond funds – such as the Short Term Bond Index Fund, Short Term Investment Grade Fund, and the Short Term Corporate Bond Fund.

For 6-10 years, we use a variety of funds such as the Target Retirement Fund, and Wellesley (because the stock allocation is of extra large Value stocks). Also for this category we would consider the Life Strategy Conservative Growth Fund. Of course with this group our main investment is in the Total Bond Market Fund, with the others hopefully boosting returns over time.

For more than ten years, stock funds such as the Total Stock Market Funds, Total International Stock Market Fund, and the S&P 500, with a few exotic funds to spice things up such as the REIT. This portion is relatively small, as we will allocate our retirement duties to primarily bond funds, with a few funds such as what I mentioned before in the 6-10 year period. I look at the stocks as a really long term investment in the event more money is needed, but I will do some rebalancing of that bucket to take profits and put money in when the market falls.

What would be your suggestions? How many buckets and which funds go into each bucket?

Principle number one when it comes to crafting a portfolio is that it’s the whole portfolio that matters. This is why, for instance, it rarely makes sense to look at one account in isolation. And it is why the overall portfolio allocation is the important question here — both what allocation you want now, and how/if you want that allocation to change over time (i.e., your intended glide path).

Bucket strategies are psychological tools, not financial ones. That is, a bucket strategy can be helpful if:

  1. It helps you to arrive at an overall allocation (and glide path) that you’re happy with, or
  2. It helps you to stick with your overall allocation (and glide path).

For example, some people may find that the easiest way to settle on an allocation is to think of it in terms of buckets (e.g., “I want 3 years in short-term bonds, 7 years in intermediate term bonds, 15 years in stocks”).

And some people may find that having a bucketing strategy helps them to feel more comfortable sticking with the plan during a bear market (e.g., “I don’t have to worry about my stocks going down, because I have X years worth of spending in short-term bonds and Y years in intermediate term bonds”).

And some people may find that a bucket strategy may be the most intuitive way for them to implement a desired glide path. For instance, if you like the idea of a “rising equity” glide path (i.e., one in which your stock allocation rises over time, as suggested by Wade Pfau and Michael Kitces here), you might find that the most intuitive way to implement that glide path is via a bucket strategy in which you do not “refill” the shorter-term (bond-heavy) buckets (by selling stocks and buying bonds) as they get depleted over time.

But if you find that managing/crafting a bucket-based portfolio is harder than just focusing on the overall allocation, then it’s best to forget about the buckets.

What you’re describing sounds to me like it may be more funds and complexity than is necessary. Maybe that’s because of the buckets; maybe not.

For instance, you asked whether the Vanguard Ultra Short Bond Fund is too risky, and whether the portfolio should have at least one year in money markets. My questions there would be: how much of the portfolio is in the Ultra-Short Bond Fund? And how much would the portfolio’s overall volatility be affected by moving part of that money into a money market fund? (My guess would be “a relatively small portion” and “hardly at all.”)

And with regard to what you consider the 3-6 year bucket, what is the specific advantage (to the overall portfolio) of having three different short-term bond funds rather than just one?

Or more broadly I might ask, can you achieve the overall risk profile that you want using just a few funds (e.g., Total Stock, Total International Stock, Total Bond)? If not, why not? What specifically do you feel would be missing? (Alternatively, what do you feel that you’d have too much of?) And how could you fill that gap in as simple a way as possible?

For instance, if you like the idea of a larger helping of short-term bonds than you’d have with the Total Bond Market Fund, what about those three funds, plus a short-term bond fund? Would anything feel distinctly missing (or overweighted) then? (And if so, again, how could you correct whatever feels “off” in as simple a way as possible?)

Let’s assume for a moment that you would find those four funds to be sufficient. In that case, the portfolio could be thought of as a short-term bucket with a short-term bond fund, an intermediate-term bucket with a total bond fund, and a long-term bucket with total stock and total international stock funds. Or we could achieve the same thing by looking at it from the overall portfolio allocation perspective (e.g., 15% short-term bond, 25% total bond, 40% total stock, 20% total international stock).

If you find buckets to be helpful, great. But be sure, after creating a bucket-based plan, to step back and look at the whole thing at once.

  • How does the overall allocation look? Does it seem reasonable?
  • How will it change over time (i.e., will the equity allocation be roughly steady, increasing, or decreasing)? Do you like that?
  • Is there a way to achieve the same overall goal with fewer funds?
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