# Retirement Ratio: Portfolio Performance and Uncertainty Measurement

My Comments: This was written a couple of years ago, but the message will resonate today with many people. For those who have expectations of retiring at some point, there is an incentive to accumulate as much retirement money as possible. All the while being sensitive to how that money is put to work.

The article is a little heavy on the math, so if you’re an engineer, this will not faze you. If you’re an English major, perhaps a little bit. But I encourage you to make the effort anyway.

A fundamental argument is that your money has to grow at least as fast as inflation, otherwise in terms of purchasing power, you are losing ground. In days past, we used to talk about the safety of Certificates of Deposit where the interest rate might have been 4%. Lost in the discussion was that inflation was 3% and taxes consumed more than 1% of the interest, which meant you were simply going broke safely.

Today, the markets are as uncertain as ever. But it doesn’t take specific knowledge or total acceptance of risk to allow yourself to think that an annual rate of return over the next several years can be in the 7% – 9% range. Click on the image that accompanies this post to get an idea what I’m talking about.

April 20, 2011 by Lowell http://itawealthmanagement.com/author/lowell/

What is the Retirement Ratio (RR)? I never heard of such a ratio, at least as it is defined below. Before going into an explanation, let me digress and address similar ratios. Portfolio performance measurements that combine both return and risk are readily available to investors. The Sharpe ratio is perhaps the best known “efficiency ratio” where it measures the amount of return earned per unit of risk. This Wikipedia reference may be easier for ITA readers to make sense of the Sharpe Ratio.

Scrolling down the Wikipedia Sharpe ratio page, one sees other performance/uncertainty measurements. Those of interest are Jensen’s Alpha, Treynor ratio, Information Ratio (IR), and Sortino ratio. Of these five ratios, my favorite is the Sortino although the Information Ratio is used for portfolios tracked using the Captool software. It is possible to extract performance and volatility data from Captool to come up with a ratio that closely approximates the IR.

Originally, the Sortino ratio was written as follows.
S = (R – MAR)/DR where
R = portfolio return
MAR = target return or Minimal Acceptable rate of Return.
DR = downside risk (DR sets the Sortino Ratio apart from other Return/Uncertainty ratios.)
MAR was changed to DTR™ for reasons given below.

In Chapter 3 of “The Sortino Framework for Constructing Portfolios” page 24 I quote, “I think the Sortino ratio was an improvement at that time in that it measured risk as deviations below the investor’s DTR™. What we now call DTR™ was called MAR in the original Sortino ratio. Attorney’s advised Sortino Investment Advisors (SIA) of a potential liability because referring to something as a “minimal acceptable return” could lead people to think we were promising that return at a minimum, so we changed it to DTR™.” Note that Desired Target Return™ is now a trademark term. One can only hope the entire English language will not be trademarked over the next 100 years.

One very important difference with the Sortino ratio (SR) is the denominator or Downside Risk. Instead of using the common mean-variance, the SR uses a semi-variance calculation. Why is this so important? Instead of measuring the portfolio volatility both above and below a mean, the semi-variance calculation only penalizes the money manager for downside risk, hence the DR designation.

The importance of DR came to my attention through two sources. 1) “Wealth Management” by Harold Evensky and 2) Captool software manual.

Quoting Evensky, “When Markowitz wrote his paper on Modern Portfolio Theory (MPT), he noted that a measure of distribution known as semivariance would, theoretically, be the best measure of risk. At the time, most computers did not have the computational power to handle semivariance. Consequently, Markowitz opted for the more practical measure of mean-variance. Today with greater computational power available at very low cost, there is an increasing interest in considering more complex solutions to investment issues, including the use of semivariance.” I suspect the difficulty of programming semivariance with the computers of the 1950s was a major hurdle as well as inadequate computing power.

The second source that peaked my interest in semivariance is more obtuse and it comes from the Captool manual. In describing Sigma (Standard Deviation) it is defined as follows. “This is a measure of the volatility of an investment’s ROI performance, and is often considered a good indicator of the investment’s risk. It is computed as the standard deviation of a number of ROI performance observations for the security or portfolio being evaluated. This standard deviation should not be confused with other, more simplistic standard deviation measures of an investment’s price. These suffer as a measure of risk, in that they penalize upside price movements as well as downside movements. Captool’s “sigma”, on the other hand, does not penalize consistent upward price movement. Furthermore, it is superior to simplistic price-based “Ulcer Indices” in that those can fail to properly handle price movements due to dividend distributions. Distributions are properly accounted for by a total return on investment measure such as is computed by Captool.” While I don’t know exactly how Captool calculates their Sigma, I strongly suspect it a semivariance calculation as it does not penalize “consistent” upside volatility.

With this background, we finally come to describing the Retirement Ratio (RR).
Retirement Rato = (P – R)/DU where
P = Internal Rate of Return (IRR) of Portfolio
R = Greater of either the IRR of Benchmark or the sum of Inflation Rate plus Retirement Withdrawal Rate. We currently use ITA Index, a customized benchmark.
DU = Downside Uncertainty or the semi-variance of the benchmark. I prefer the term, Uncertainty, as it does not carry the variety of meanings laid on the term, Risk.

This form of the ratio looks identical to the Sortino ratio only we use R instead of DTR™. R sets a higher standard than Desired Target Return (DTR™).

A little more detail or description of R is in order. To determine R, we are looking for the greater of two values. The first value we look for is the Internal Rate of Return of the benchmark. If P > R, then the portfolio is performing better than the benchmark. This is a desired goal, but extremely difficult to reach as active mutual fund managers well know.

The second value we look for is Retirement Target Return. The second form of the Retirement Ratio looks identical to the first form shown above, only we substitute Retirement Target Return (RTR) for R. Exactly what is the RTR? It is the sum of the current inflation rate plus the percentage the investor needs or anticipates withdrawing from the portfolio during retirement. Normally this value ranges from a low of 0% plus inflation to a maximum of 5% plus inflation. Should we experience deflation, that would factor into this form. Anything higher than a 5% withdrawal rate greatly increases the probability of the retiree running out of money. Withdrawal rates around 2% to 4% are recommended.

To calculate the Retirement Ratio, and this is built into the TLH spreadsheet, we use an IF THEN equation to look for the higher of either the IRR for the benchmark or RTR.

If the Retirement Ratio is greater than zero, we have a high probability of not running out of money regardless what the market is doing. To check this logic we also run a Monte Carlo calculation based on another set of variables. The Monte Carlo analysis gives us a long-term probability picture while the Retirement Ratio informs us how well we are doing from month to month and year to year.

Should readers need an example to better explain the Retirement Ratio calculation, you only need to request it in the comments section and I will go through a few with assumptions. Many times examples shed light on difficult concepts, and the RR is a tad complicated.