This is part 2 of the series about building an asset allocation framework. We will expand on the previous work which was based on NIFTY50 index and compare the previous work to a similar analysis of NIFTY500 index. We will also have a look at 7/10 year rolling CAGR for both the indices, this was missing in the previous post.

Our asset allocation framework is based on the above-mentioned equity index, it can be successfully applied to the majority of stocks in the market, but there will be few stocks which will be in a bull or bear market of their own due to their own unique reasons. So if you are an individual investor in direct equities, you should know your holdings before applying this framework.

This framework can work successfully for mutual fund SIP investors as they can direct their SIPs to debt assets during market highs and switch to equity assets during market falls. Unfortunately, most SIP investors do not want to spend even 5 minutes analyzing anything about markets, and that is why we need good financial advisors who can allocate their client’s hard-earned capital into appropriate asset classes at the right time.

**Simplest Strategy**

Markets tend to move from extremes of undervaluation to overvaluation and back all the time. The charts below are proof of that. The charts below represent the movement in PE of the NIFTY50 & 500 indices over their lifetime.

A very simple strategy could be to slowly start reducing equity allocation of your portfolio when the index PE percentile starts crossing above 80% and slowly start increasing equity allocation when the index PE percentile starts crossing below 30% percentile *(these are rough guesstimates from the charts, one can use PE as well instead of percentile).* I lay emphasis in slowly because no one can time the peaks and troughs perfectly, but if you can use this framework and get the market cycle even somewhat right, you should be ahead of buy and hold strategies.

You will also notice in the charts above, that the markets can both bottom and peak at different PE and percentile, there is no set rule that the market follows. Even the PE ranges we have of 10-30 are based on historical data, there is no guarantee that the market won’t blow through these ranges in the future.

To make better sense of which PE falls in which percentile we plot the PE movement with percentile in the charts below to see where the current PE stands compared to the historical PE range. One can clearly make out the extremes at the left and right tails of the PE curve.

NIFTY500 PE Curve

**Introducing Historic PE to Rolling CAGR**

While all that is good to know, we need to make sense of what these numbers mean for our expected returns. Until we match the above data with their respective rolling period returns we cannot ascertain with precision which PE or percentile returns are the best to invest in and which are the worse to stay out of.

This is where the following scatter plots come in. These charts plot all the rolling returns of specific time periods against their starting period PE. If you do not know what rolling returns are, please google or read part 1 on this blog.

From the trendlines of the charts, one can see the obvious that an investor makes higher returns when their capital enters the markets at lower PEs relative to entering at higher PEs. This is the basis of our entire asset allocation framework.

Another interesting observation is, how the scatter plots shift to positive returns territory as one expands one’s investment horizon. Therefore, in equity asset class it really pays off to buy at cheaper valuations and to have a longer time horizon.

While the scatter plots help us identify certain trends from the whole population, we need to dig further into the data with some filters to make sense of it all.

**Aggregating the Data into Distribution Ranges**

We accumulate the PE and their respective rolling returns data into distribution ranges. In the charts below, we divide the whole PE range into 20 subsets which represent 5% percentile range each. This helps compress the entire scatter plot into one line.

We can now use this data to build our asset allocation framework, we can use a certain return threshold that we expect from our investments and avoid the valuations which on average will yield lower than expected returns.

NIFTY500 Average Rolling CAGR

If you are of the belief that averages hide more than they reveal the particulars of a dataset, I have further probability analysis based on win-loss scenarios in the table below.

Following the same distributed PE ranges as in the chart above, we represent the median, maximum and minimum return over these ranges.

I believe that 15% is the minimum return any equity investor should target at the minimum for taking equity asset risk. This belief is what guides my analysis in the tables below. In the average and median CAGR columns, the green highlights represent returns above 15%. Between 15% to 9% are in yellow and below 9% are in red.

If you were to go by average and median CAGRs, the distribution suggests that anywhere below ~17 PE for NIFTY500 & NIFTY50 are good times to buy into the equity markets.

Coming to the maximum and minimum columns, I included these to represent what the averages and medians do not, these tell you how good or bad your returns can get at the extremes and one should be mindful of reversion to the mean. The maximum column is telling us that at PE ranges above 27.5 for NIFTY500 and 23 for NIFTY50, even if you get the biggest bull market possible, your returns will be low. Similarly in the minimum column, if you are ever able to get the market at below 11.55 PE for NIFTY500 you cannot lose across all timeframes even at the worse extreme.

NIFTY50 Percentile Return

Now we come to the most interesting part of the analysis, the next few columns represent the win-loss scenario and winning probability over different time periods. We define a winning rolling period which gives us greater than 15% and any return below that is considered a loss. So across the PE distribution ranges, we find out the number of wins and losses. The Win/Loss and win probability columns represent the same concept, Win/Loss is a simple division where any value greater than 1 or 100% represents the odds of winning are in our favour, while in win probability this is represented by the probability of a win crossing above 50%.

If we use win probability of 50% as the threshold for exiting the markets, for NIFTY50 suggests that above PE ranges of ~18 that odds start turning against you. This is similar to the findings from averages data. But should we use a PE of 18 to get out of the market completely? No, because PE of 18 and above represents ~68% of the market trading days. That is a whole lot of market to stay out of.

Another fact is, that the market cross 18 PE in two different directions, once it is climbing to 18 PE and higher from below and one it is falling to 18 PE and lower from above. These can represent a bull and bear market respectively and our averages just sum these two results up. So we need to go higher in the PE range or lower in the win probability to mark market exit points.

If we look at the probabilities for PE ranges above 23 for NIFTY50, we see that for 3/5 year periods the probability of a winning outcome is essentially 0. For 1 year periods, there are still some chances of winning but above 25 PE range, those diminish as well. For 7/10 year periods, the chances of winning reduce dramatically at PE ranges above ~25 and ~21 respectively. So one can start an equity exit plan when market PE reaches above 20, our exit strategy can be staggered in increments of 5% of the portfolio as the market PE inches higher little by little. This should ensure that you exit equities within 12 to 18 months.

Similarly, once market PE starts dipping below 18 we can start adding incremental amounts of capital into equities. Going in a staggered manner will ensure that you do not lose out on all the gains as the market inches higher from high PEs and also that you do not exhaust all your capital before a market bottom.

This strategy is not fool-proof, the markets do not always touch the historic peak or bottom PEs in mid-market cycles, so you won’t be always right, but it will ensure that majority of your capital is allocated in the right assets.

NIFTY500 win-loss reveal somewhat mixed results, for 3 year time periods probability of winning above PE of 19 is very low, however, over 5 years, we see some revival in winning probability in 23-26 PE range. We can ignore this anomaly because the winning probability despite the odd rise is still low.

In the 1 year time periods, there is an outlier at the 26-27 PE range. I am guessing a lot of the times the market rallies higher from this range. The 7/10 year time periods yield, completely different result than that of the NIFTY50. Here, there is a good revival of winning probabilities in the 20-27 PE range. I am not sure how to resolve for this anomaly, these anomalies represent 25% of the total dataset.

The NIFTY500 index has seen these PE levels only thrice for the 7/10 year rolling data. These were in 2000, 2007 and briefly in 2011. The index spent a lot of time between these PE ranges from 2015 onwards but this data will not start showing up in our 7/10 year rolling CAGR until 2022/2025 respectively.

In the last two charts, I have added a column at the end which gives a representative figure on what your equity allocation could look like at different PE ranges. This is not a recommendation but a representation of how to use the data. In the last post, we received the feedback that a few people still could not understand how to use the framework on the final step. Therefore, I have provided this representation at the end. My equity allocation matrix is different from the one represented here, so please make your own.

I have provided high-resolution images of all the charts in the link below.

Google Drive Link: Charts

Data Source: