Volatility-Adjusted Mutual Fund Selection

Volatility-Adjusted Performance Measures

by Werner W. Gansz

Many mutual fund managers achieve above-market returns by the simple expedient of increasing the portfolio’s volatility.  This is a poor way to achieve higher returns.  There is no value-added to this approach when considering long or intermediate term holding periods since statistically, the amplified downside risk will eventually compensate for the amplified upside opportunity.  The penalty for being on the wrong side of the market is proportionately enormous. 

A better fund selection strategy is to pick fund managers that achieve above-market returns with less than proportional increase in portfolio volatility.  A volatility-adjusted ranking system penalizes portfolio returns of funds with higher than market volatility.  The Sharpe Ratio is a very conservative measure of excess returns (over the cost of money) vs. absolute volatility.

NCAlpha

In 1998, the author developed a more aggressive volatility-adjusted performance measure called NCAlpha, which reduces the achieved daily returns of the fund by the returns of the relevant market index, amplified by the relative volatility of the fund to the market index.  If a fund’s daily returns are twice as high as the index and its daily volatility is twice has high as the index, its volatility-adjusted return is zero.  Since NCAlpha is based on relative volatility and is tied to a market index, high NCAlpha-ranked funds may be more volatile but achieve higher returns that those for the Sharpe Ratio.

Both of these performance measures are based on the verifiable idea that in a managed fund’s volatility (and especially its relative volatility vs. the target index) is a fund characteristic that is controllable by the manager and therefore is relatively consistent over time. 

Below is an article on the effectiveness of volatility-adjusted performance measures.  It is Part 2 of the article on Small Caps  I use a database called FastTrack® to provide mutual fund and index data as well as several 3^rd party programs that use this database.  Some of the discussion below assumes familiarity with the jargon of these programs.

Using the Small Cap Indices as a Guide to Investment Productivity

Volatility-Adjusted Performance Analysis

The first part of this article focused on the use of the small cap indices as guides to identifying productive market environments and discussed a methodology for building a list of mutual funds that responds reliably and vigorously to these productive environments.  A simple AccuTrack® ranking methodology was suggested as one way of making final selections from that list of candidates at the start of each productive market cycle.  Part 2 will focus on the use of volatility-adjusted ranking systems to better control the volatility of the resulting portfolio while maintaining a high level of productivity. 

“It’s the (Total) Portfolio, Stupid!”

	AccuTrack® trading history	Ann	UI	Mdd
FAMA		60.98	5.07	19.27
FAMA2	1/2 invested in AccuTrack® plan		2.41	09.94
FAMA3	2/3 invested in AccuTrack® plan	39.39	3.28	13.02
NCALPA	NCAlpha trading history	57.81	3.18	10.04
Sharpe	Sharpe trading history	53.07		12.6

Table 1. Comparison of Various Methods of Volatility Control

In Table 1, FAMA summarizes the 6-year portfolio history of the AccuTrack® trading plan discussed above and in the prior article.  Note that the Mdd, which has grown over the 2½ years of real time history, is now approaching 20%.  A risk-averse investor could easily decide that this Mdd is too difficult to live with.  One option is to invest less than the full portfolio to reduce the volatility.  If 10% were a more tolerable Mdd target, maintaining 50% of ones portfolio in money market would achieve this reduction in Mdd, shown in FAMA2.  However the penalty in Ann is a dramatic halving of returns.  An Mdd is a single event in the life of the strategy.  A better plan might be to try to reduce the routine drawdowns that occur with this strategy rather than focusing on Mdd.  Drawdown volatility can be measured by UI.  Maintaining a 2/3 investment in FAMA (FAMA3) to bring UI down to a more manageable level, still results in a significant reduction in Ann.

The last two rows in Table 1 summarize the performance of two types of volatility-adjusted ranking and trading systems (to be discussed below) measured over the same time frame.  Note the similarity in Mdd and UI to the partially invested plans.  Attempting to control volatility by remaining partially invested in a MM is clearly an extremely inefficient process.  And, as will be shown later, enhancing returns by up-leveraging volatility is also an extremely inefficient process.  What this table suggests is that if you are investing in strategies that are so volatile that you have to de-leverage your investment to hold it through the inevitable short-term corrections that occur within a typical intermediate-term cycle, you may win the bragging rights at the water-cooler for having the highest return strategy but your total portfolio returns will be severely constrained because the strategy is too volatile for your risk profile.  There are some very good fund managers out there who know how to extract very high returns from relatively low levels of volatility.  Holding those funds with 100% of your portfolio and holding them only during productive market environments is a far more efficient method of volatility control. 

The Sharpe Ratio

Dr. William Sharpe developed a method of portfolio analysis that combines the portfolio’s historical returns with its volatility.  This is not the place for an elaborate mathematical treatise but in simple form the Sharpe Ratio is the portfolio returns achieved over a period of time less the cost of borrowing the money to buy the portfolio, divided by the Standard Deviation (volatility) of the portfolio;

Sharpe ratio=(Returns of fund – Margin Interest Rate) / StdDev of fund

Clearly the Sharpe Ratio demands that market returns come from something other than increasing volatility.  Simple arithmetic will show that a 50% increase in returns created by a 50% increase in standard deviation is a loser.

This ratio can be used as the basis of a ranking system that measures the fund manager’s performance more than it measures the fund’s performance.  Since the intent of this plan is to be invested only when we are in a productive market environment and we have pre-selected funds that we know are most likely to respond to that environment, then using the Sharpe ratio to find the best volatility-controlled fund managers will help to ensure that the investor can remain 100% invested through the entire cycle.  The row labeled “SHARP” in Table 1 is a ranking and trading strategy based onthe Sharpe ratio.  Note the very low UI with only a modest reduction in Ann over FAMA.

NCAlpha 

Another form of volatility-adjusted ranking recognizes that volatility is a market phenomenon that every fund manager (and investor) must live with and rewards those managers that can outperform the market with less volatility.  A market index is used to represent the broad market.

NCAlpha = Returns of fund (Stdev of fund / Stdev of index) * Returns of index

This means that simply outperforming the market (Returns of fund – Returns of index) is not good enough.  If the volatility of the fund has to be increased to create those excess returns, NCAlpha requires that the index’s returns be increased by the relative standard deviation of the fund to the index before making the comparison.  In effect the index returns become those that could have been achieved by the mere leveraging of its volatility to equal that of the fund.  If the fund can do no more than achieve the same returns as the leveraged index, we don’t need a fund manager at all; anyone can leverage an index.  If a fund performs equally to the reference index but has higher volatility, its NCAlpha will be negative.  If a fund has twice the volatility of an index and has twice the return, its NCAlpha will be zero.  That’s no big deal; any high beta index fund like UOPIX can do that (with NDX-X as the index).  (In reality, a leveraged index fund will always have a negative NCAlpha when compared to its index because real fund expenses and trading inefficiencies reduce returns below those of the perfect leveraged index of the same volatility.)  If a fund has the same returns as the index but does it with less volatility, it will have a positive NCAlpha. 

NCAlpha is a variant of the alpha term used in Modern Portfolio Theory to build stock portfolios.  Alpha uses “beta” in place of the relative standard deviation term in NCAlpha.  Beta merges standard deviation with the investment’s correlation to the reference index.  It allows for de-correlation of the components of the portfolio to reduce the apparent volatility of the portfolio.   For mutual fund portfolios taking advantage of productive markets defined by strong small cap performance periods, de-correlation of the few funds within the portfolio is neither relevant nor desirable.  When the small caps signal a buy, all the funds in the portfolio are supposed to salute smartly and charge up the hill.  In these portfolios the only real volatility control is real volatility control, not de-correlation.  For this reason, the correlation term in beta was removed, leaving only relative standard deviation to define NCAlpha’s (Non-correlation alpha) volatility ratio.

Relative Volatility

 A fund’s relative volatility compared to the market is selected and controlled by the fund manager.  It is a very stable characteristic of the fund.  Performance however, is not stable.  It fluctuates with market dynamics and manager skill.  Figure 1 highlights 5 years of TVFQX performance vs. WIL-S, the reference index.  The yellow line, TVFSD, is the relative standard deviation of TVFQX to WIL-S over the 5-year period.  Since FT charts are all percentage change charts, it is clear that fluctuations in the relative standard deviation are small in comparison to the broad sweeps of bull and bear cycle performance of the fund and the index.  Relative standard deviation provides a stable base from which to measure a manager’s ability to convert volatility into returns.  It is no accident that TMCGX has approximately the same standard deviation as WIL-S while VWEGX has twice the standard deviation.  Those are management decisions.  As will be shown in the next section, each of these fund managers is nearly equally adept at converting the fund’s selected volatility into returns commensurate with the risk that they take. 

Figure 1.  Comparing TVFQX (red) and WIL-S (green) performance to the Relative Standard Deviation of TVFQX to WIL-S, TVFSD (yellow).

 What Does a Good Volatility-Adjusted Fund Look Like?

 The poster child for excellent volatility-adjusted performance these past few years has been TMCGX.  Its volatility is only slightly higher than WIL-S, the reference index for NCAlpha, yet its performance is a sparkling 70% Ann when included in a RUTTR-based trading strategy.  NEEGX seems to have found the same formula for success.

                                               Ann        UI    NCAlpha

                                       --------  --------  -------

WIL-S  INDEXFAM Wilshire SmallCap         26.41      5.08   reference

TMCGX  Turner MicroCap Growth             70.50      5.67     0.15

NEEGX  Needham Growth                     71.29      5.31     0.11

TVFQX  Firsthan Technology Value         109.98      6.36     0.12

VWEGX  VanWag Emerging Growth            101.43      7.15     0.11

PBHEX  PBHG Select Equity                102.20      9.29     0.07

RYSIX  Rydex Electronics/44               64.60      8.23     0.05

PBTCX  PBHG Tech & Communications         97.38      9.77     0.04

UOPIX  ProFunds UltraOTC Investor Sha     89.72     14.31    -0.09

MGFQX  Millenni Growth                    78.49     12.47    -0.05

 Table 3.  

Moving up a notch in volatility, TVFQX and VWEGX are certainly earning the extra volatility that they create, less so with PBHEX and PBTCX.  These two funds do very well but at a price in volatility that seems unjustified in comparison to the others.  RYSIX and UOPIX do not compete in this league, either for performance or volatility reasons.  If the investor has the intestinal fortitude to hold UOPIX through an entire intermediate term buy cycle, then he/she doesn’t have to worry about volatility-adjusted performance measures.  For mere mortals however, TMCGX’s 70% Ann with a UI of 5.7 will win out over UOPIX’s 90% Ann with a UI of 14.3 anytime.  With a basket of funds like TMCGX in the portfolio, it is far more likely that the investor can withstand the short term corrections that always occur during strong markets without selling in panic at the bottom and then losing out on the next leg of the cycle.  A fund like MGFQX has no redeeming social value whatsoever. It is little more than a high-beta index fund in disguise.

A Picture Perfect 6-Pack

Figure 2 highlights the characteristics of 6 exceptional funds, VWEGX, TVFQX, BJMIX, TMCGX, FUSMX, and NEEGX.  The charts are fnu’s of each fund’s performance only during strong small cap markets as measured by RUTTR; they are in MM during sell periods.  Most importantly, each fund responds reliably and vigorously to each new cycle.  The summer 2000 bear market rally caused some problems for FUSMX, but the rest got over their mid-cycle jitters and moved higher. 

Figure 2.erformance of 6 Funds During RUTTR buy periods: VWEGX, TVFQX, BJMIX, TMCGX, FUSMX, NEEGX.

Summary

 The key points of this two-part article can be summarized as follows

Invest when the small caps are moving. Small cap indices are our canaries in the mines. When they are happy and singing, get invested

Pre-select candidate funds for reliability and performance during strong small cap markets. A reliable list of pre-selected candidates reduces the likelihood that the final portfolio will not respond immediately to the next strong small cap market and improves the odds that the portfolio will remain strong throughout the buy cycle.

Build a plan with which you can stay 100% invested through the entire cycle.

Partial portfolios or, worse yet, unplanned mid-cycle exits, are terribly inefficient no matter how “hot” the funds are.

Selecting funds by volatility-adjusted performance increases the likelihood that the investor can maintain a fully invested position start-to-finish through the inevitable short-term corrections that occur during intermediate-term cycles.