The Performance Analytics' PAR Model changed to a positive stance in June, with the six-month expected return for the S&P 500 (NYSEARCA:SPY) of 3.1%.

Accordingly, we are changing our recommendation to an Overweight to public equities - a change from our Underweight recommendation that was in effect in the last three months.

The PAR Model is a factor model designed to estimate the expected equity return over a six-month period. The model is based on a dynamic multi-factor regression of the S&P 500 returns over economic, valuation and market variables. The factors are chosen each month as part of the model run, based on their statistical significance, from the set of 15 factors that have proven to be significant over time.

S&P 500 6-m expected return: 3.1%

Recommended allocation: Overweight

Prior month -4.4%

Change 7.5%

**Significant Factors**

The P/E ratio is one of the key measures of index valuation in the model. It continues to exert a significant positive contribution to the model's expected return, at 0.9 standard deviations (S.D.) This is partly offset by the negative impact from our proprietary measure of Earnings Quality (see definition), at -0.6 S.D.

We use the P/E ratio that is based on the trailing 12-month index earnings, due to its statistical significance in predicting the incremental index movements as part of the model. The P/E ratio based on forward estimated earnings does not work as well, because analyst revisions add random variability to this measure.

The healthy trend in U.S. corporate earnings contributed to the below-average P/E ratio, and in turn, to its positive contribution to the model's expected return of around 1 S.D. in the last two years. Most recently, profits increasing by 6.1% YoY in Q1-2012 (which was much higher than analysts' estimates).

The P/E ratio rose slightly in June, to 13.8, driven by the rally in index of about 4%. It remains very attractive by historical standards, being well below the five-year average of 15.6. This explains why the P/E provides a significant positive contribution to the expected return as part of the model.

The following trends are worth watching, as they will affect the future EPS and P/E. It appears that earnings will grow at a slower rate than expected in Q2 and Q3, driven by the European recessionary environment and by slower growth in the U.S. and everywhere else in the world. Analysts continue to revise down their Q2 2012 earnings estimates, now estimated to grow at 3.0%, compared to the estimate of 4.3% as of last month, and to 6.3% as of March 31st.

The ratio of positive to negative Q2 EPS pre-announcements is so far 28/74, worse than average at this point in the reporting cycle. Excluding Bank of America, the largest contributor to Q2 earnings growth for the index (due to the large loss a year ago), earnings growth becomes negative, at -1.7%.

The Price/Book ratio is a significant factor in the model, even though it is not as widely followed by the market. Its current contribution to the expected return is 0.4 S.D.

Among the economic group of factors, only Industrial Production has a positive impact on the expected return, of 0.7 S.D. It improved considerably so far this year, from 0.3 S.D. at the end of 2011.

The ECRI Weekly Leading Index and Durable Goods Orders are still at levels at which they extend a negative influence on the model's expected equity return, of -0.6 and -1.1 S.D., respectively.

The ECRI WLI in particular is worth watching closely this year, in our view. As the index improved to 126.6 in March, its contribution to the model's expected return improved to almost-neutral -0.1 S.D.; however the index dropped back to 121.5 in June.

The price of crude oil dropped again in June, to $85 from $86.5 in May, and from above-$100 levels in the previous three months. Its contribution to the expected return, while still negative, improved significantly, now at -0.8 S.D., up from -1.1 S.D. in both March and April.

The model measures the impact of oil price on the equity index returns directly, rather than trying to infer it from the economic effect. It accounts for both the price level and the timing, i.e. the effect of how long prices stay high or low. It is intuitive that it takes time for high (or low) oil prices to have an impact on the market, as it takes time for prices of refined products to react, and for these to have an impact on consumers. The current trend looks very positive for equities - if oil price stays at the current level or goes lower, it will have a significant positive impact of the expected return.

Our proprietary measure of Momentum takes into account the speed with which factor contribution to the model is changing. The effect of Momentum on the expected equity returns was close to neutral in June, at -0.1 S.D.

We follow active asset allocation strategies that are based on the expected equity return signal from the model. If the expected return is positive, the exposure to the equity index is increased, and if it is negative, the exposure is reduced relative to the benchmark. Four strategies are followed (all equity exposure if achieved via long/short positions in SPY):

1. Fixed Bands - the exposure to public equities is symmetric: either 120% of the benchmark exposure (overweight by 20%), or 80% (underweight by 20%).

2. No-Leverage - the active exposure can only be reduced, but cannot go above 100%, i.e. no leverage is allowed. This strategy may be suitable for pension funds and other portfolios in which allocation to equities is limited by investment policy.

3. Variable Bands - the active exposure is proportional to the strength of the signal by the PAR Model, while capped at +/-20%. For example, an expected return of 5% would generate a modest overweight, but 25% would generate the maximum overweight of 20%.

4. 100% Active Switching - fully invests either in the equity index, or in cash - this is an extreme case of strategy #2.

**Disclosure: **I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.