Beyond the Ultimate Death Cross
July 31, 2012
by Georg Vrba, P.E.
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Last week, I showed why the “ultimate death cross” is not a bearish signal. But the methodology behind that signal – what’s known as a “goldencross trigger” – can indeed offer a reliable guide to investors. And one can do even better with a simple improvement to the trigger that I have devised.
The basic goldencross trigger occurs when the 50day, shortterm average of a stock or index moves above its 200day, longterm average. I modify this slightly to get something I call the ”moving average crossover” (MAC) system, which I’ll explain in due course.
Its results are impressive. An asset allocation strategy based on the MAC system provided, on average, a 40% higher return than the basic goldencross trigger would have offered. Historical investment results from this MAC system have been, on average, 2.4 times higher and less risky than a buyandhold (B&H) investment in an S&P 500 index fund. The strategy is easy to implement and should be useful for retirement accounts.
In appendix A are the probabilities calculated from likelihood ratios for market gains and losses following MAC signals; it shows why I selected the particular moving averages that I chose for my MAC system.
I used daily data from January 4, 1965 to July 6, 2012. Investment results are with dividends reinvested. For the S&P, dividend information comes from Robert Shiller’s S&P data series; reported dividends were reduced by 5% to account for fund fees. When not invested in the S&P 500 index fund, I assumed funds were held in the Vanguard GNMA fund (VFIIX) from its 1980 inception onwards, and before that I used a money market account paying interest at the Federal Funds Rate. For the calculation of moving averages I used trading days, not calendar days.
The investment strategy
My MAC system works as follows, with a buy signal and a sell signal triggering shifts from investment in the markets to the safer, moneymarketfundlike reserve.
Buy signal for the S&P 500
 A buy signal occurs when the 34day exponential moving average (EMA) of the S&P 500 becomes greater than 1.001 times the 200day EMA. (See appendix B for calculation of the EMA.)
Sell signal for the S&P 500
 A sell signal occurs when the 40day simple moving average (MA) of the S&P 500 crosses below the 200day MA.
There were 28 buy signals from 1966 to 2012, the most recent occurring on January 3, 2012. Buy signals didn’t count when they occurred during the period while the previous buy signal was still in effect, which resulted in only 24 useable buy signals out of the 28 possible; they are listed in appendix C together with their corresponding sell signals.
There were 28 sell signals from 1966 to 2012, of which 23 followed a previous buy signal. The most recent occurred on August 12, 2011.
When a buy signal occurs, the whole investment goes into an S&P 500 index fund, and when a sell signal occurs all the funds are moved from the S&P 500 index fund to a GNMA fund. It’s that simple.
Investment results
To simulate this strategy over longer periods, I began with $1.00 in a GNMA fund (or a money market account, prior to 1980) on the first day of every year from 1966 to 2010. I then transferred the money to a S&P 500 index fund when the first buy signal occurred. I then calculated the terminal value for each year’s $1.00 investment, in all cases through July 6, 2012.
Starting with a dollar during each of the 45 years from 1966 to 2010, one would have invested a total of $45 cumulatively by the end. Summing the 45 terminal values, this strategy would have netted this dollarperyear investor a tidy sum of $2,502. Following a B&H strategy in the S&P 500, one would have only $835, about a third as much. (The basic goldencross system would have produced about two times more than the B&H strategy, but still a good deal less than the MAC system.)
The final value of the investment accrues in a few ways: from capital gains (or losses) following the model’s buy signals, reinvested dividends while in the stock market, and both the capital gains (or losses) and reinvested dividends from the GNMA investments (or interest from a money market account prior to 1980).
Had one made the first investment in January 1990, instead of 1966, he or she would have invested a total of $21 by now. The sum of the 21 terminal values to July 6, 2012 was $102, versus $53 for the B&H strategy in the S&P 500. (The basic goldencross system in this case would have produced 1.61 times more than the B&H strategy in the S&P.)
The table below lists the internal rate of return (IRR) for the $1 annual investments obtained from the MAC system, the buyandhold strategy of the S&P 500, and from a money market account.
Modified goldencross system: S&P500 returns with dividends reinvested  when not in S&P500, funds are invested in a GNMA fund with dividends reinvested. 



B&H money market at Fed Fund Rate 
B&H S&P500 
modified golden cross MAC system 
B&H money market at Fed Fund Rate 
B&H S&P500 
modified golden cross MAC system 







number of investments 
45 
45 
45 
21 
21 
21 

total invested 
45 
45 
45 
21 
21 
21 

sum of terminal values 
$124.17 
$835.00 
$ 2,502.34 
$ 32.49 
$ 52.52 
$101.79 

IRR 
3.82% 
9.88% 
13.13% 
2.05% 
7.17% 
11.95% 
for periodic investments 
max IRR 

15.66% 
13.79% 

15.66% 
11.95% 
min IRR 

3.81% 
9.04% 

3.81% 
9.04% 

average IRR 
2.23% 
8.10% 
11.79% 
1.28% 
6.33% 
10.17% 

standard deviation 

2.68% 
1.70% 

2.95% 
0.90% 

Sharpe ratio 

2.19 
5.64 

1.71 
9.84 


period 
1966 – 2012 
1990  2012 