These days a lot of macro discussions are focusing on rising interest rates. Will the Fed taper? When will they taper (seemingly next week)? And what will happen to markets when they do, in particular what will happen to equities?

Conventional wisdom says that rising rates are bad for equities. There are lots of justifications of this claim the main one (that we like and think makes sense) is that rising rates mean a higher "risk-free" rate which means higher interest rates on fixed income products from savings accounts to 30-year bonds (yield curve assumptions aside). Ultimately, the qualitative thought behind this argument is that as rates rise the average Joe will see higher yields in fixed income products and will opt to put more of his money into some kind of interest bearing account (savings, money market, CDs, notes, bonds, etc.). When that excess capital goes into the various interest bearing vehicles, the money will have to come out of whatever vehicles it was parked in. Conventionally, the thought is the money will come out of equities thus lowering stock market returns. This, of course, makes logical sense, if I can get a high yield with "no risk" why risk the volatility inherent in the stock market, especially against the often frightening macro backdrop offered these days. At the same time, higher yields will incentivize Joe to save not spend thus impacting the economy in a negative way.

However, despite this completely logical argument, we can make a counter claim, which is equally logical and convincing. The claim would be that if the Fed does taper and rates rise that means things are on the mend in the economy and that means companies are doing better and things are otherwise getting better. So if things are getting better we should probably expect equity markets to keep marching up indefinitely-better economy means better things for the companies which make up said economy means better sales>earnings>valuations.

While each of these arguments is compelling and could be used to justify action, we prefer to find out what lessons history tells, in particular what historical data tell us about the relationship and what we might expect going forward based on historical outcomes.

We examined monthly data on 2 and 10-year yields and the S&P 500 (NYSEARCA:SPY). We calculated simple percentage change returns, comparing this month's S&P 500 return to last month's 2 and 10-year yield change. We did this because we were trying to determine what happens to stock returns after rates rise. In order to determine what happened "after" rate changes historically, we would have to see what happened to the S&P 500 the month after the various rate changes. Below are two charts, which show the scatter diagram relationship including a simple linear regression line.

Taking the original stance, that rising rates hurt subsequent equity market returns, we would expect to see a downward sloping regression line meaning when rate changes last month were high (rates went up last month), equity market returns this month would be low (stocks went down this month). The inverse would also apply meaning rate decreases would likely prompt strong equity market returns. Examining the scatter diagrams and regression lines above, we see in the case of the 2-year yield the regression line is basically flat with a negligible R squared (measure of how well the data predict one another). In fact the regression line points ever so slightly upward, contrary to popular wisdom that rate increases stunt equity market returns. In aggregate, there is really no relationship. Looking at the 10-year chart above, we again see a regression line that is basically flat. Again the R squared is very low at 0.008. Here the regression line exhibits the downward slope we would expect to find given the assumption that rate increases prompt lower equity market returns but again the relationship is incredibly small.

We decided to go one step further and examine the average S&P 500 returns in all weather, then post the up and down rate change periods. Below are two tables examining the relationship. The tables display the average S&P 500 return, the number of up months (aka months with a positive return) the number of total months, and the % of up months. The S&P 500 returns are separated into all months combined then by whether the prior month rate changes were up or down.

Here we see the effect we expected. S&P 500 returns are lower, on average, in the month following a move higher in both 2 and 10-year rates than they are in the periods following a move lower in 2 and 10-year rates. Stated simply, average returns seem to be worse after rates increase. The percentage of up months was higher following a decline in rates yet more than half of the month's returns were still positive after a rise in rates (i.e. % up was still >50%).

We decided to dig a little further and examine the distribution of the returns following the rate increases. Our suspicion was that there may be a few outliers dragging the average returns down.

We decided to strip out the bottom 5% of returns to see what the average outcomes would look like. We did this then recalculating the averages and found the new average for the S&P 500 (post an increase in 2-year yields the month before) to be +1.08%, well above any of the averages in the tables above. We interpret this to mean the perceived lower returns that result after an increase in 2-year yields are really more a function of a few very ugly "crash" type months. Meaning if you are betting on a lower return in the S&P 500 after a rise in 2-year rates you are really betting on a few big magnitude moves lower-this is an outlier, which is typically a bet we don't like.

Performing the same analysis on the 10-year yield (dropping the bottom 5% of S&P 500 returns post an increase in the 10-year yield the prior month) we found the new average to be +0.76%. In this case the new average is still well below the +1.08% average return experienced in the S&P 500 after a fall in 10-year yields (note the +1.08% in this paragraph and the prior paragraph focusing on 2-year yields are different). We interpret this to mean that equity market returns do in fact experience lower returns in months following an increase in 10-year yields. However, those seeking to express this bet need to keep in mind that more often than not (56.6% of the time) S&P 500 returns are still positive in the months following a rise in 10-year yields and on average returns are still positive.

**Conclusion:**

S&P 500 monthly returns appear to be lower on average in months following an increase in 2-year yields the prior month but this is largely the result of a few outsized negative S&P months. When these months are excluded, the average return actually exceeds the average experienced following decreases in the 2-year yields. **Betting on relative underperformance in stocks the month after a rise in 2-year yields is really a bet on a crash, which is a low probability bet.**

**Regarding 10-year yields, stated simply, S&P 500 returns are better on average in months following a decline in 10-year yields and worse in months following a rise in 10-year yields.** However, those seeking to exploit this phenomenon should know that average returns are still positive in the months following a rise in 10-year rates and more than half (56%) of months still had positive returns so going short may not be the best idea.

This time could of course be different but for those inclined to make equity market wagers based on interest rate changes; we believe this study should be a useful guide.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it. I have no business relationship with any company whose stock is mentioned in this article.