Is it right time to buy?

Investors often ask this question is it the right time to buy? And there are no clear answers to this questions. Yet it is important to answer this question. Market participants use various matrix to judge the valuation of the index. The most commonly used matrix is price to earnings ratio (P/E) which can be calculated by dividing the Index by trailing 12 months earnings per share.

This ratio is simple and intuitive to use. Whenever P/E is high the markets are trading costly hence it’s better to reduce position and whenever the P/E ratio are low the markets are trading cheap hence its better allocate more capital to equity. But P/E ratios are not without its issues.

The problem is also to identify at what level the P/E ratio signifies richly valued markets or extremely cheap. There are no clear cut answers to this problem. Moreover when P/E ratio are trading at extreme levels there is either euphoria or panic in the market and people hardly have courage to increase/reduce allocations in those conditions.

Example of excessive optimism is 1992 and 2008 while examples of excessive pessimism is 1998 and 2003. Although economic tells us that we are rational beings, humans are emotional and irrational. Hence we need a mathematical model to take asset allocation decisions which does gets impacted by the extreme exuberance or pessimism prevalent in the market.

It would be prudent for long term investors who can shift their capital from debt to equity when markets are undervalued and vice versa.  This will not only minimize volatility but will also reduce the pain of seeing one’s portfolio in deep red when market corrects.  And if done correctly this will also significantly enhance returns for long term investors.

So lets us deal with the problem in calculating P/E ratio. As P/E is price/earnings let us examine how each of this component impact the calculation of P/E ratio.

Price as we all know swings between euphoria and panic. Price is a dependent variable in our model and is directly observable in the form of index.

Earnings is an independent variable and Earnings depends on lot of factors but the most important of them all is economic conditions. As we all know that there are business cycles where economy goes into rapid expansion and slow growth or stagnation/recession.

EPS growth rates rises rapidly during expansion and is higher than the trend growth or sustainable growth. As soon as the economy slides back into slow growth or recession phase EPS growth reduces or contracts below the trend growth or sustainable growth rate. Hence EPS itself went into the cycle of boom and bust which has immense impact on the calculation of PE Ratio.

In the below chart we can see the difference between the trend/sustainable EPS which I have termed as true EPS V/s Observable EPS or EPS data declared by the index. True EPS is simply the base EPS multiplied by the compounded annual growth rate of long term EPS growth. From 1993 – 2016 EPS Growth was a CAGR of 13.5% which roughly equates to the GDP Growth rate of 7% and inflation of 6% during this period. For calculating the Trend/Sustainable EPS I have assumed the base EPS to be 10 and P/E of index 10X when the index was constructed in in the beginning of 1979 

As we can observe in this chart whenever there is rapid economic expansion the observed EPS moves way above the true/sustainable EPS and when the economic conditions reverses observed EPS falls back to the level of sustainable EPS. This happened twice since 1993. Frist instance was from 1993 – 2000 and the second instance was from 2004 - 2008

Hence instead of using the observed EPS for calculating the P/E ratio I have used the true/Sustainable EPS to calculate the P/E ratio which I have termed as True P/E of index.

As we can see from the chart whenever the index trades close to 10X to 12X true P/E ratio it forms a long term bottom which happened in 1984. 1988, 2003. Whenever True P/E is trades above 40X this calls for a serious market sell off which happened in 1991 – 1992 and 2007 – 2008.

Here I must point out that the P/E ratio may look grossly exaggerated but this is because they are calculated using the true/sustainable EPS. As I have mentioned earlier whenever economy goes through a period of rapid economic growth the EPS expands way above the sustainable growth rate which in turn subdues the observed P/E ratio of the index.

If we look at the given chart we can see the difference between Observed P/E and True P/E. from 1995 – 2001 the observed P/E of the market is well below 20X but the true P/E of the index continues to trade between 20X to 40X.

Similarly from 2004 – 2008 the observed P/E of the market is between 10X to 22X while the true P/E ratio of the index moves from 13.7X to 47X

 Using true P/e instead of observable P/E ratio negates the impact of economic boom and bust on the EPS and helps us true gaze the the correct valaiton of the market.

This model is itself not without faults or criticizm. The primariy being

1.       The CAGR rate for the future may be different then the CAGR rate of the past but this can be adjusted in the model. I will use the long term infaltion expecations + long term GDP growth rate as future growth rate for EPS

2.       The current EPS which is used to calcuate CAGR may be subdued due to economic down trun or may be excessively high due to economic boom which in trun will impact the CAGR.

3.       The base EPS may be incorrect which will change the true P/E calcuation.

4.       Future market multiple can be significantly different from past market multiples.

All these are valid critisim of the model but they can be negated by using the model in a proper way which will take care of these limitations.

I have created a model using P/E ratio which can help a long term investor exploit the market swings between excessive fear and excessive optimism. I have assumed that the investor has the capability to switch from equity to debt when markets are richly valued and he can create leverage when markets are cheaply valued.

In the below table we can see median P/E multiple for the market

Valuation	Upper Range	Equity	Cash
Median	22.7	100%	0%
+1 Sigma	30.3	75%	25%
+2 Sigma	37.9	50%	50%
-1 Sigma	15.1	115%	-15%
-1.5 Sigma	11.3	130%	-30%

As per this model we will never go 100% in cash or take excessive leverage. We will increase exposure when markets are trading cheap and reduce exposure when the markets are trading at rich valuations. The base exposure of the portfolio is 100% if the market is trading between -1 Sigma median to + 1 Sigma median of True P/E i.e. between 15.1X to 30.3X. If the true P/E moves above 30.3X then reduce equity exposure to 75% and if true P/E moves above 37.9X we will reduce equity exposure to 50%.

Similarly when true P/E falls below 15.1X we will create a leverage of 15% and increase exposure to 115% and if true P/E falls to 11.3X we will increase our exposure to 130%

Conservative investors can avoid using leverage but they can increase the allocation to equity and reduce allocation to debt in their portfolio when market trades below 15.1X or 11.3X of true P/E. To reduce the frequent rebalancing of portfolio I prefer to use the average of last 5 quarters of true P/E to make allocation changes.

My average exposure to equity from 1979 - 2016 would have been 96%.  During market corrections i.e. from 30/12/1992 to 30/9/2001 when Index went sideways the exposure to equity would have been 71% while during the correction to 2007 – 2008 the exposure to equity would be 56%.

Hence if an investor follows this model to control his exposure in the market there can be substantial increase in the upside while reducing the volatility and drawdown at the same time.

Investors can change various parameters of this model according to their risk appetite. They can either be aggressive or conservative in managing their equity exposure.

In the first chart I have shown the equity exposure since 1979 and in the second chart I have shown the equity exposure from 1992 – 2002

 Equity exposure from 1979 - 2016

Equity exposure from 1992 -2009

I have also calculated the unlevered portfolio returns. The unlevered portfolio returns by using this method by simply allocating between cash and equity would be 18.1% CAGR compared to 16.3% for the index. Over a period of 37 years this would amount to almost 1.77X index returns with much lower drawdown and volatility.