**Asset Allocation For Retirement**

**Introduction**

**Introduction**

This article will examine a key issue for all investors – how to adjust the equity and fixed income proportions of your retirement portfolio as you approach and enter retirement. The goal is obviously to have enough capital built up in your retirement account so that you can live comfortably throughout your retirement. There are two forces that you must contend with to achieve this goal. First, your portfolio must significantly outpace the rate of inflation which will deteriorate your buying power over time. Secondly, you must deal with volatility – when your time horizon shortens, you won’t be able to make up large losses that could occur. We will begin by looking at some advice from trusted professionals then discuss the aspects of this decision in more detail. Finally, we’ll give the Sigma Investing recommendation for an investor with an average risk appetite.

**Sound Advice from Trusted Experts**

**Sound Advice from Trusted Experts**

Let’s start by examining some advice from experts whose opinion we trust. The below list is not exhaustive but we feel that it gives a reasonable overview of the opinions that you would encounter when consulting a high quality financial advisor. We will use these recommendations to start the discussion on how to think about shifting your asset allocation over time.

Here are our experts:

**Vanguard**– We believe that Vanguard is an excellent institution which has investors’ interests as their primary focus (they are a non-profit after all). We will use their Target Retirement funds as a basis for their recommendations.**T Rowe Price**– T Rowe Price isn’t our favorite mutual fund company but they have done some credible research on the risks of running out of cash in retirement based on different allocation strategies.**Burt Malkie**l – Malkiel is the author of “A Random Walk Down Wall Street” and works as a professor of Economics at Princeton.**Charles Ellis**– Ellis is the author of “Winning the Loser’s Game” and is a long-time consultant to the investing industry.**Seeking Alpha**– Seekingalpha.com has a section on the benefits of passive, index fund-based investing. They present a cogent and compelling case for this strategy. Their asset allocation adjustments are recommended by their founder David Jackson.

The table below shows the portion of the investor’s portfolio which should be allocated to equity investments while the remainder is assumed to be invested in bonds (or money market funds in some cases). Of course, we believe that the equity portion should be divided amongst US equity, foreign equity and REITS while the fixed income should include treasury bonds as well as inflation-protected treasury bonds.

It’s clear from reading this table that all of the advisors recommend a gradual transition from portfolios heavily allocated to equities to an eventual portfolio which is dominated by bonds and other fixed income instruments. Ellis is the most aggressive – he believes that young people should take the higher volatility that accompanies high equity allocation since they have a very long time horizon plus they have the future earnings power to overcome setbacks. On the other hand, Seeking Alpha is the most conservative of the set. Their equity percentage at age 65 is half that of Ellis. It’s interesting to note that the Vanguard and T Rowe Price suggestions are almost identical. We believe that these are probably all reasonable approaches – but we will perform some analysis to verify this statement later in this article. Next, we will explain the tradeoffs between volatility and outpacing inflation that these allocations are implicitly making.

**Issues to Consider**

**Issues to Consider**

The core objective for investors is to allow their savings to grow more quickly than inflation while avoiding the risk of having their cost of living significantly impacted by a market downturn in their later years. Thus, the general approach is to have a large proportion of your retirement savings dedicated to equities in your youth and reducing this as you approach and enter your retirement.

**Two Primary Investment Risks**

In “Asset Allocation”, Roger Gibson gives an excellent discussion of the key tradeoffs in various asset allocations and how the two primary investment risks to portfolio are:

Inflation – Inflation is basically a force that will shrink the purchasing power of a portfolio. It is a primary concern for fixed income investments where rates of return are lower.

Volatility – Volatility is a measure of the stability of a portfolio’s growth over time. This is most serious in equity instruments where rates of return are more volatile.

**Inflation**

Since most fixed income instruments (especially those recommended by Sigma) don’t produce expected returns that are much higher than inflation, the destructive power of inflation to your portfolio will be significant if you are heavily weighted towards fixed income. If you invested completely in an intermediate term treasury fund and were earning about 5% returns per year, your portfolio may appear to be healthily growing. However, when you factor in the impact of 3% inflation, you will realize that it would take you 35 years for you to double the spending power of one dollar invested. If your portfolio grows at this real rate, then you will have to save a very large amount of your income to support your retirement spending.

**Volatility**

To counter the risk of inflation, equities are vital to your portfolio since their historical returns have been significantly higher than fixed income securities. This higher rate of return is vital since it will allow you to work fewer years and build up a sufficient retirement fund while outpacing inflation. Creating a solid gap in your equity returns versus the rate of inflation allows your investments today to become significantly more valuable in real terms in the future. If you have a 40 year time horizon and can earn a rate of return 6% greater than inflation, each dollar that you invest today will be worth $10 (in real terms) when you need it. That is a powerful investment vehicle for long term portfolios.

However, increased volatility is the price of these higher equity returns. The S&P 500’s annual return since 1928 averages about 9.5% per year but the standard deviation of annual returns is about 20%. That means that about 1 out of every three years will produce returns of -10% or worse. For young investors, volatility is not that bad. They don’t need the money anytime soon so they can afford to patiently wait for the market to rebound. However, this volatility is a major risk to older investors whose primary objective becomes to maintain a constant (in real terms) or steady stream of income from slowly selling their holdings after they enter retirement. A couple of very down years can put them in serious danger of running out of money.

By considering these two risks, it makes sense that the best course of action would be to heavily invest in equities while your time horizon is long to take advantage of expected returns with should comfortably outpace inflation. Then, as the investor transitions into retirement, the percentage of portfolio assets allocated to fixed income investments should increase to reduce the potential negative impact of volatility.

**Funds Required for Retirement**

Building a portfolio over the course of the investor’s working life requires a large amount of savings. Many advisors recommend withdrawing 4% of the total value of your portfolio in the first year of retirement then increasing that amount by the rate of inflation. So, if you want to withdraw $50,000 (in real terms) for your living expenses, you’ll need a portfolio valued at $1.25M (also in real terms). If you want to withdraw $100,000 then your portfolio must be valued at $2.5M. So, these are sizable amounts of money – even if spending $50,000 per year in living expense doesn’t sound lavish. So, aggressive saving during one’s lifetime is a must. Saving 10-15% of annual salary is a good general guideline.

**Sigma Investing Recommends**

**Sigma Investing Recommends**

While we believe that the strategy of progressively increasing the amount of fixed income in your retirement portfolio makes sense, we want to perform some testing on the various approaches to determine what might be the best rate to increase the fixed income exposure. In this section, we will examine 5 different plans which are similar to those put forward by our experts. We will focus on measuring the probability that the investor does NOT run out money while spending it in retirement. We will make some reasonable assumptions and conduct simulations to judge the effectiveness of these strategies. First, let’s take a look at the portfolio which we will be comparing.

If you compare these strategies with those offered by our experts, you will note that the Conservative Strategy is similar to Seeking Alpha. The Core Strategy is very close to the strategy of Vanguard, T Rowe Price and Malkiel. Finally, the Very Aggressive Strategy mimics Ellis’ plan. We feel that analyzing these strategies will give us good insight into the benefits and risks with each.

**Key Assumptions**

For each strategy, we have conducted 10,000 simulated lifetimes as the investor ages from 25 to 95. We assume that the investor is saving from age 25 to 65 then making withdrawals from his portfolio for the remaining 30 years. To create annual returns on his portfolio, we have drawn (with replacement) an annual S&P 500 return and treasury bond return from the historical record of 1928 to 2009. So, our model does depend on the future being broadly similar to the past in overall rates of returns and volatility for these two asset classes. We think that is a fair assumption. Here are our more detailed assumptions:

The investor saves $7,400 in the first year and his savings contributions grow by 5% each year. These figures were not chosen randomly. They represent the amount of savings required to hit a target retirement portfolio balance of $1,250,000 in real dollars at age 65 if the investor earns consistent annual returns of 9.3% in equities and 5% in fixed income using our core strategy. We targeted this target retirement portfolio balance since it allows a 4% withdrawal to be equal to $50,000.

We study two different rates of withdrawals in retirement. At age 65, the investor withdrawals either $50,000 or $62,500 in real dollars and this amount increase each year by the rate of inflation.

The annual rate of inflation is 3%.

The investor adjusts his proportion of equity and fixed income every five years.

The investor rebalances every year.

The investor has no other income (pension, social security, real estate, etc.).

Based on these assumptions, we ran our simulations and measured the success of investors in terms of being able to make their targeted withdrawals each year in retirement without running out of money.

**Success Probabilities**

Now, let’s look at the probability of not running out of money when the investor starts with an initial withdrawal of $50,000 or $62,500 (both in real terms). Again, these initial withdrawal amounts represent 4% and 5% of the target age 65 portfolio value. It is worth noting that sometimes these rates would be higher or lower than 4% of 5% of the simulated real portfolio value at age 65 due to the simulated portfolio’s performance during the saving years of the investor.

First, let’s examine the success probabilities for the five strategies based on 10,000 simulations.

In this analysis, we see that the conservative strategy substantially under-performs the core and aggressive strategies. When starting with a withdrawal of $50,000, the investor will run out of money 18% of the time. The core strategy provides a nice improvement in probability and the aggressive strategies all perform about the same. When the investor’s initial withdrawal is larger, the conservative strategy again performs substantially worse than the others. This is likely due to the fact that a 5% withdrawal rate is somewhat high and the conservative strategy doesn’t have enough equity exposure to grow the assets significantly faster than inflation. The more aggressive strategies are progressively better without too much difference between the three aggressive strategies.

One interesting question is the relative safety of withdrawing at various initial percentages of your age 65 portfolio value. The general belief is that withdrawing at 4% is very safe. In our next analysis, we will just assume that the investor reaches age 65 with a real retirement portfolio balance of $1,250,000 (in our previous simulations, this number was variable based on the performance of the investor’s portfolio during your saving years). Now, we will see how likely the investor is to have money throughout retirement based on their initial withdrawal amount and the asset allocation strategy employed. Here are the success probabilities:

The results in these tables are interesting. First, it’s nice to see that all the strategies perform well at the 4% withdrawal rate. However, these strategies do leave the investor with a 10% chance of running out of money during retirement. That isn’t as safe as we were expecting. But, if it was to happen, the investor would likely run out of money after 25+ years. At the 5% withdrawal rate, the chance of running out of money is substantial. It’s clear that this is a risky rate to plan to make withdrawals. If the investor does decide on this withdrawal amount, it seems clear that the investor will need a higher portion of their portfolio invested in equities to give him a better chance of making it 30 years without running out of money.

**Our Recommendation**

Based on our analysis, we feel that a reasonable investor would prefer either the Core Strategy or the Aggressive Strategy. The Conservative plan performs fairly poorly and the more aggressive plans don’t have noticeably better performance than the Aggressive Strategy. We believe that the personal choice probably comes back to the stomach for risk that you possess.

The Aggressive Strategy recommends 65% equity exposure at age 65. If you turned 65 in 2008, then you might have experienced the (temporary) evaporation of 35% of your portfolio in one year. You should ask yourself: how would I have handled that? Run to large exposure to bonds? If that is a realistic answer then you would have missed the subsequent equity rally in 2009.

For the average investor, we think the the Core Strategy provides a good platform for retirement investing. The dual risks of volatility and inflation are responsibly managed and the investor stands in a good position to live comfortably in retirement. Below, we have produced a table which shows the expected levels of annual return and standard deviation which the investor can expect during their life based on historical data. We believe that these levels of return and volatility should be fairly manageable over the course of the investor’s life.

**One final note:** While it is crucial to stick to the right investment strategy for your retirement portfolio, it is just as important to have the discipline to save increasing more money during your full working career. We think that an investor should be saving 10-15% of their current earnings each year. With the right investment strategy it’s possible to retire and be very sure that your funds will last throughout your retirement. However, without the right disciplined approach to saving, you have no chance!