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In my last article, S&P 500: Sell in May & Come Back in November, we found compelling evidence from the study done on monthly returns from 1928 to 2012 that "sell in May and come back in November" is a feasible investment principle. This article presents a viable investment approach based on this principle which could be exploited by long-term and short-term investors alike to generate alpha. This strategy is nothing but developing an efficient portfolio that includes fully investing in the S&P 500 index during the entire period November to April, and then selling out and staying in cash or possibly other investment opportunities during the remaining months of the year.

In other words, the strategy fully exploits the relative exuberance of S&P 500 during the period November to April vis-à-vis its performance during the period May to October. The principle of "sell in May and come back in November" could also be applied in developing a rebalancing strategy for your portfolio that has S&P 500 as the core part of your portfolio. Both the applications of the principle will be discussed later in this piece.

As you may recall from my previous article, a dollar invested in 1928 in S&P 500 using this principle would have become $34.18 today, at an annual rate of return of 4.2% in the last 85 years. On the contrary, if we had stayed invested in S&P 500 only during the period May to October during those years, a dollar invested in 1928 would have fetched you merely what you had invested. If we look at figure 12 in that article, this anomaly or if you wish to call it - "the effect" - has been pronounced since the late sixties. So in order to substantiate this effect further and to find better insights into other anomalies outlined in my earlier article, I undertook a further study of the monthly returns of S&P 500 for a narrower time-frame - 1960 to 2012.

This article unearths the data from that study, which for all purpose, eliminates the extreme volatility that was inherent in the monthly returns in the inter-war years. The study has been captured as far as possible in the twenty-one charts as well as three tables outlined in this article below, so following them in tandem with the article would give you a better insight into the study undertaken. The charts are very useful in enhancing your understanding on how the monthly S&P 500 returns have been trending across various time slices for each month of the year.

Sell in May and come back in November: The study revealed that a dollar invested in 1960 in S&P 500 using this strategy would have fetched you $23.07 today, at an annual rate of return of 6.1% (see figure 1). Conversely, if you had stayed invested in S&P 500 during May to November, and stayed on the sidelines during the remaining months of the year, your original investment would not have budged at all.

To closely understand the dynamics behind this phenomenon, we can look at figures 2, 7, and 8. In figure 2, the historical analysis from 1960 shows that the months from November to April exhibit significant positive average monthly returns for S&P 500: Novembers with an average return of 1.3%, Decembers 1.6%, Januarys 1.1%, Februarys nearly nil, Marchs 1.1%, and Aprils 1.4%. Relatively, barring Octobers, no other month in the May-to-October time-frame exhibits significant positive average returns, and even worse Septembers (-0.7%) and Junes (-0.2%) averaged returns in the red. To analyze ever further on granular scale, I sliced the last fifty-three years into three time frames of: last ten years, last twenty years and last thirty years. As you can see in figure 3, on average the weakness in the returns of S&P 500 during the months from May to October continue to remain resilient in all those time frames.

For thirty-eight of those years since 1960 (see figure 4 and figure 5), the performance of S&P 500 during the period November to April surpassed that from May to October - that's about 71% of the time. As you can see in figure 4, during those years, S&P 500 outperformance in the November-to-April periods averaged 11.8%. Conversely, in the remainder of the years, S&P 500 underperformed during the period from November to April by an average of 8.6%.

What if we are long S&P 500 during November to April and short S&P 500 during the rest of the year? The study revealed that a dollar invested in 1960 in S&P 500 using this long/short strategy would have fetched you an abysmal $2.84 today (see figure 1). This approach is not much better off or in fact equally worse when compared to the approach of investing in S&P 500 only in the period May to October.

October is just like few other months in the financial calendar: If we consider the measures, the number of two-digit monthly declines of S&P 500, Octobers and Septembers share the top honors each experiencing two such episodes since 1960 (see figure 6). In the same time period, S&P 500 has declined 40% of the Octobers with an average decline of 4.0% compared to the 55% of Septembers at an average decline of 3.8%. Conversely, it grew 45% of the Septembers with an average growth of 3.3% compared to the 60% of Octobers when the large-cap index expanded at an average of 4.1% (see figure 7 and figure 8).

Furthermore, if we consider the average of the top five declines of S&P 500 for each of the months in a year since 1960, Septembers perform better with an average decline of 9.7% in contrast to a poorer average decline of 11.8% unveiled by Octobers (see figure 9). However, on the positive front, Octobers have registered a top five average increase of 11%, with Septembers registering a modest average increase of 5.9% (see figure 10). Consequently, we can gather that S&P 500 has been extremely volatile in Octobers; in the long run overall extreme episodes of decline in Octobers have been matched by episodes of extreme spikes, with the latter having an upper edge pushing the average return for Octobers to the positive side.

As you can see, figure 11 confirms this assertion as October has the highest monthly volatility among all the months with an annualized 20.6%. Albeit Septembers pale in comparison to Octobers in terms of risk (volatility of annualized 15.4%), by and large S&P 500 during Septembers have dropped an average of .7% since 1960 compared to its average expansion of .9% during Octobers (see figures 2, 7, and 8). So, from the point of view of long-term investors, it can be reasoned that Septembers too, apart from Octobers, are jinxed. The study shows that Octobers have been volatile in the post-war years, though not as volatile as in the inter-war years as revealed in the earlier study (see figure 11).

After excluding the volatile episodes of the inter-war years in the newer study, and taking into account together the measures volatility and the top five average declines, in returns of Octobers since 1960 vis-à-vis that of other months of the year during the same time-period, short-term traders still may have reason to fear Octobers. But, to call October jinxed is little bit farfetched in view of the data (review table 1 and table 2) we have at hand. Besides, if you look at figure 7 and figure 8, performance of S&P 500 in Augusts has been worse than that of Octobers with an average decline of 4.3% since 1960.

Likewise, Januarys with an average decline of 4%, and a high volatility of 17.5%, are in the same boat as Octobers. However, Januarys and Augusts do not carry the negativity that Octobers carry in the financial calendar, notwithstanding the fact that like Octobers, monthly returns of S&P 500 since 1960 also have been in the red 40% of the time for each of those months. To add to the mix, the Julys, which have spent 55% of the time during the same time period in the red with an average decline of 2.7%, are not spoken in the same fearful breath as Octobers either. The myth that Octobers are scary perpetuated from the great crash of 1929, and was reaffirmed by some hefty declines of S&P 500 in Octobers (as discussed in the earlier article) during the depression era. But, since the actual index in the current form came in to being in 1957, there have been only two major drops in Octobers:

  1. 21.8% during the crash of 1987 (see figure 12)
  2. 16.9% in 2008 during the "Great Financial Crisis"

So now, after having analyzed the various measures on display in the charts, we have sufficient understanding to refute that the month of October is distinctively jinxed, or in fact, if you want to word it otherwise, to prove there are a few more months in the calendar that are equally as fearsome as Octobers.

Table 1: Summary of the historical analyses of the monthly returns of S&P 500 from 1960 - 2012

(click to enlarge)

"January effect" is not in play anymore for large caps: Since 1960, S&P 500 has declined 40% of the time during Januarys with an average decline of 4.0%, while it declined 25% of the time during Decembers with an average decline of 2.2%. Then again S&P 500 grew 75% of the time during Decembers with an average growth of 2.8%, while S&P 500 grew 60% of the time during Januarys at 4.4% (see figure 7 and figure 8). Cumulatively, in the same time period, S&P 500 grew on an average 1.6% in Decembers compared to the 1.1% in the Januarys (see figure 2).

From the perspective of volatility, December is the safest month, as it ranks last among all the months with an annualized monthly volatility of 11% (see figure 11). If you review figures 3, 13 through 15 and table 2, we can conclude that the bump that S&P 500 used to receive in Januarys is not pronounced any more, and in fact Decembers have been performing relatively much better in the recent years and thus begs the question whether the "December effect", from either spiked consumer spending in Decembers or increasing number of investors taking advantage of sell-offs in Decembers, has been more dominant in the recent years. But, one should recognize that in the modern day with high-speed internet and program trading, no market anomaly can be exploited for an indefinite amount of time. With free flow of information, any anomaly that rises disappears with passage of time depending on the efficiency of the market in question.

Table 2: Profile of the Monthly Returns

(click to enlarge)

Portfolio analysis: Let's consider three portfolios - portfolio 1, portfolio 2, and portfolio 3. Portfolio 1 built using a core security say for example SPX, the readily available S&P 500 index product, where the portfolio is fully invested in the security during the months May to October every year and then for the remaining months of the year, it is fully invested in cash. Likewise, portfolio 2 is built using the same index product, but is fully invested in the security from November to April during November to April and in cash for the remaining months of the year. However, portfolio 3 built from SPX is fully invested in the security throughout the year. Let's review table 3 to see how the portfolios would have performed since 1960 and since 1997. (Please note: return on cash investments are set as nil, but that would not be the case in actuality. The returns of S&P 500 are used as proxy for computing the returns of the portfolio.)

  1. Portfolio 1: If you had invested $1 in 1960, at the end of October this year, the portfolio would have ended with a terminal value $1.06, excluding taxes and transaction costs. The portfolio would have yielded an average of 0.6% per annum with a volatility of 9.6%. Similarly, a $1 invested in 1997 would have ended with a terminal value of $0.81 at an average annual yield of -0.5% and a volatility of 12.5%. On a cumulative basis, the portfolio would have had an effective annual yield of 0.1% and -1.3% respectively with the two scenarios.
  2. Portfolio 2: If you had invested $1 in 1960, at the end of October this year, the portfolio would have ended with a terminal value $23.07, excluding taxes and transaction costs. The portfolio would have yielded an average of 6.6% per annum with a volatility of 10.8%. Similarly, $1 invested in 1997 would have ended with a terminal value of $2.46 at an average annual yield of 6.3% and a volatility of 10.5%. On a cumulative basis, the portfolio would have had an effective annual yield of 6.1% and 5.8% respectively with the two scenarios.
  3. Portfolio 3: If you had invested $1 in 1960, at the end of October this year, the portfolio would have ended with a terminal value $23.58, excluding taxes and transaction costs. The portfolio would have yielded an average of 7.5% per annum with a volatility of 16.4%. Similarly, $1 invested in 1997 would have ended with a terminal value of $1.91 at an average annual yield of 6.0% and a volatility of 19.4%. On a cumulative basis, the portfolio would have an effective annual yield of 6.1% and 1.2% respectively with the two scenarios.

Using figures 19 and 20, and as was discussed earlier, we can rule out portfolio 1 from the mix. So from the portfolios we are left with that are equally performing, we need to make a determination which one of the remaining two is superior and in order to do that we'll make use of table 3.

  1. In terms of the risk measure - volatility, one can strongly conclude portfolio 3 is more risky than portfolio 2 for both the time periods 1960 - 2012 and 1997 - 2012. This conclusion is also confirmed by figure 20, where the red line, which represents the progress of the value of portfolio 3, is very choppy from the middle of the nineties.
  2. From the perspective of the average annual performance (see table 3), during the period 1960 - 2012, portfolio 3 triumphed over portfolio 2 with the former registering an average annual return of 7.5% compared to the latter's 6.6%. However, in the time period 1997 - 2012, portfolio 2 (6.3%) edged portfolio 3 (6.0%) by 30 bps.
  3. And from the viewpoint of terminal value and effective yield (see table 3) for the time period 1960 -2012, portfolio 3 prevails with a value of $23.59 and an effective annual yield of 6.1%. However, for the time period 1997 - 2012, portfolio 2 with a terminal value of $2.46, and with an effective annual yield of 5.8%, edges portfolio 3. In terms of terminal value and effective annual yield, no convincing selection of portfolio can be made.
  4. However, using coefficient of variation (risk per unit of return), portfolio 2 comes out ahead for both the time periods convincingly (see table 3) with lower risk per unit of return - 1.6 for 1960 - 2012 and 1.7 for 1997 - 2012.

Since the annual returns, both effective and average, for both the portfolios are nearly in the same ball park, portfolio 2 would be the best choice as it endures less for a unit of return (lower coefficient of variation). In other words, portfolio 2 is more efficient than portfolio 3.

Two-season portfolio strategy - As we have discussed above, portfolio 2 does not outperform portfolio 3 convincingly in terms of average annual returns, as primarily, portfolio 2 is only active for six months of a year. In order to make up for this inadequacy for long-term investors, we need to build a portfolio called "Portfolio-X" that is made of two blocks:

  1. Block 1: made up of the efficient portfolio 2, that would exist in the portfolio from November to April and then cease and desist through its sale at the end of the period. The proceeds of the sale would be used to fund Block 2.
  2. Block 2: made up of a portfolio made of any asset class that can beat the benchmark portfolio 1. In the last fifty or odd years, portfolio 1 returned an average of 0.6% per annum, and for the last 15 years, it has averaged -0.5% per annum (see table 3). Block 2 would exist from May to October and then cease and desist through its sale. It is essential that the block has a coefficient of variation that is similar to block 2 or at least less than portfolio 3, to make this strategy a viable alternative to portfolio 3. The proceeds of the sale would be rolled back to fund Block 1. Outperforming portfolio 1 with such average returns should not be a challenge at all.

The approach we have used here in building Portfolio-X is what we may designate as the two-season portfolio strategy (two-seasons because portfolio allocation switches after every two seasons). We have already discussed the exuberance of S&P 500 during November to December, but the key element in Portfolio-X is identifying a set of securities or index from any asset class that would outperform S&P 500 during May to October (i.e. portfolio 1), and keeping their coefficient of variation lesser than that of portfolio 1's (otherwise S&P 500's). By doing so, we'll have a Portfolio-X that is efficient and outperforms S&P 500 generating valuable alpha for long-term investors. Some logical choices for securities that would go into Block 1 would include low-duration, high-coupon investment grade corporate bonds.

Another interesting portfolio approach could be when S&P 500 is core part of a portfolio, and end of months May and October are used as time-triggers to balance the portfolio. Therefore, the portfolio could be rebalanced overweighting S&P 500 at the end of October and underweighting it at the end of April.

Table 3: Portfolio Analysis

(click to enlarge)Note: Return on cash investments is set as nil, but that would not be the case in actuality.

For sake of brevity, this article does not dwell in detail on the performance of S&P 500 in each of the months of year. But, the graphs as well as the tables should help you draw conclusions on S&P 500's performance across various months of the year, and help generate ideas for short-term investors. Specifically, if you want the compare the study done for the period 1960 - 2012 with that done for the time period 1928 - 2012, you can review figures 16 through 18.

Conclusion: The undeniable evidence that we have gathered from this discussion is that during the November-to-April time-frame, S&P 500 on average performs significantly better than the rest of the months of the year. This anomaly or "the effect" could be used by short-term investors to make significant gains in their investment portfolios. However, a feasible long-term portfolio of S&P 500 constructed from this anomaly is what we defined in this article as the "two-season strategy". This strategy is effectively a mechanism for long-term investors to translate the principle "Sell in May and come back in November", first outlined in my previous article, in to higher returns for their investment portfolios.

Based on the average positive return of S&P 500 for Januarys (4.4%), Februarys (2.6%), Marchs (3.1%) and Aprils (4.4%) in the last fifty or so years (see figure 8), we can expect to see S&P 500 touch 1600 by end of April if the fiscal cliff is averted. S&P 500 could end up lot higher, if the potential grand fiscal bargain between the White House and the Congress involves extension of the tax rates for dividends, capital gains and estate taxes outlined in the Bush tax-cuts.

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Source: Two-Season Approach To Building Efficient Portfolios Using S&P 500