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Empirical evidence supports the argument that the Dividend Discount model is more useful than that of the Federal Reserve in explaining market movements. So much so that with an accurate forecast of both the dividends of the DJII and the yield of the 30 year T Bond, the Price of the DJII can be correctly forecast at least 83% of the time. Using the Fed model of earnings and the long bond yields it is only 36%.

Recommended Action: Buy DIA and Bank of America (NYSE:BAC)

Given that this paper is in part about the positive impact of rising dividends, and there is a high probability of Bank of America being allowed to re-instate its dividend within the next year, last summer's "'Dog of the Dow" could well be the surprise of the year ahead. It has already doubled over the past 12 months, but is still a long way from its 2006 all-time high of over $53 per share, let alone making new highs like the DJII.

Efficient Market Hypothesis - Not So Efficient

The Efficient Market Hypothesis asserts that stock markets are efficient. The price is thus always right and the facts have to be changed to fit the thesis rather than the other way. In the case of the market, the facts may tell us that the price of market is either above or below its value and this provides an opportunity to either buy or sell shares that are either under- or over-priced.

The Dividend Discount Model suggests that the Efficient Market Hypothesis has been correct only 83% of the time over the past 30 odd years. The conclusion is that since March 2009 we have had, and still have, one of the greatest buying opportunities of all time resulting from "Irrational Pessimism" spawned of FEAR that has yet to dissipate fully.

Value and price are not always the same as shown in the first chart below. Between 1981 and 1995 they were 96% of the time. In the latter half of the 1990s the price of the DJII exceeded its value during Alan Greenspan's period of "Irrational Exuberance" where greed ruled supreme and ended with the era of the Dot Bombs.

During that time, however, the value of the DJII kept rising and lent solid support to the price of the DJII by the early years of the millennium through 2008. The financial collapse following the Lehman catastrophe brought the price of the DJII down to a level considerably below its value as "Irrational Pessimism" took over fueled by FEAR.

Despite continuing pessimism the DJII price has been grinding higher and is already up 139% from the 2009 trough. The Value of the DJII stands at 23,329 today while the Price continues to move back to equilibrium with value. Simultaneously, the value is falling as 30 Year T Bond rates rises.

While the first chart tells the story of the relationship between price and value the question remains:

"What is the determinant of Value?"

Starting from the premise that investment is a long-term proposition and that the performance of one investment is always relative to a "riskless" return and the best way to measure this is using the Dividend Discount Model.

Common equities are irredeemable instruments. Hence, the only return on investment that a shareholder receives from a company is a dividend. Capital gains and losses come from the market and these are driven by either actual or anticipated growth in dividends and changes in interest rates. As equities are perpetual they should be measured against the long end of the bond market. In the extreme the British Consols and the like, but in practise the 30 Year T Bond yield provides an excellent proxy.

Think of equities as perpetual bonds with variable coupons, the coupons being dividends that by-and-large rise over time. Dividends are more robust than earnings which can be extremely volatile as noted particularly in the immediate aftermath of Lehman.

Dividends by comparison have been much more stable.

Price and Value

The Yield (or interest rate) on a bond = Coupon/Price or i = C/P

The price of the bond can thus be calculated as P=C/i. As the coupon is fixed any increases in interest rates i, would result in a falling bond price to bring it in line with similar but newer bonds. The converse is also true.

Replacing the Coupon with a Dividend would result in a fair Price (or Value) of an equity relative to a 30 year T bond V=D/i .

Again, as long interest rates rise the value will fall. However, if the dividend rises it could well neutralize the negative impact of rising interest rates. Should interest rates fall the value would rise in tandem with the bond market but if the dividend also rises the positive impact on value would be compounded, as was the case between 1981 and 2008.

In essence, changes in value are a direct function of dividends and an inverse function of interest rates:

Since the nadir of the bond market on September 29, 1981, it has risen 4.05 times as the yield (or interest rate) on the 30 Yr T Bond has fallen from 15.2% to 3.75%. In line with this we would expect equities to have risen by the same amount. However, the DJII dividends have also risen 6.59 times from $55.79 to $376.70. The product of the 4.05 multiple expansion, from the drop in the interest rate and the 6.59 fold increase in the dividend should result in a 26.69 fold increase in the Value of the DJII and with at least an 83% probability the Price of the DJII should also increase by the same amount.

In the event, the price of the DJII has not moved up as much as value but it certainly seems to be ratcheting upwards as pessimism dissipates. This is despite the talking heads of the media having no clue as to why the market is rising or how far it might continue. Certainly they know the price of everything but unfortunately not the value. They are confused, to say the least, by the rise in the market when the Roubini-esque economic commentators are still predicting we are about to fall into an abyss just around the corner, as they have all the way up since March 2009.

Believed to be from the New Yorker Magazine, circa 1960 judging from the shape of the TV and the rabbit ears,

Dividends much less volatile than Earnings

Dividends have been more robust than earnings as corporate directors are reluctant to cut dividends in line with falling earnings. Cuts or the elimination of dividends are viewed negatively by many institutional investors. Some pension funds and insurance companies have to sell positions in the case of dividend cuts or eliminations. Hence, when earnings fall in recessions the payout ratio moves up, even to infinity following immediately Lehman's collapse.

Despite many corporations having strong cash flows and being flush with cash, the payout ratio, at 39%, is at the lower end of the historical range. As confidence returns to corporate board rooms, and Fed permission is granted to banks, the payout ratio could rise.

Inserting here such a possibility as the only forecast in this paper, it is conceivable to see a 4.5% rise in nominal GDP in 2013 which should be sufficient to result in the DJII earnings (which are also nominal) rising by 10% to $1,000. Simultaneously, the payout ratio could rise to say 50%, (the average over the past 30 years has been 63% but that has included those years where the earnings have fallen precipitously).

A 50% payout would see the DJII dividends rising 36% from $367.55 to $500. With no change in interest rates this would push the value of the DJII to 38,500. To bring the value back down to the current price of 15.628 the yield on the 30 yr T Bond would have to more than double from 3.74% to 7.60%. It seems unlikely that the Fed will let that happen over the next year. However, if it does both the economy and inflation would be probably expanding much more than expected. So too would earnings and dividends. Which-ever scenario transpires it is highly probable that the upward pressure on the price of the DJII form 15,628 should continue.

The next chart demonstrates how both the bond yield and the equity yields have fallen over time and since Lehman the DJII equity yield has on occasion been above that of the T Bond Yield.

Furthermore, the ratio of the DJII yield to the T Bond Yield has been well in excess of the historical average of 42% for the past 5 years. A return to that level using current interest rates and dividends would require a 49% rise in the DJII to 23,329.

What a Surprise! This is the very same value level shown in the very first chart but this time on a log scale.

This is followed by an arithmetic scaled version with the shorter time frame of 2008 to 2013 when the value-price equilibrium broke down.

Commentary on the gyrations of the past year

On July 25, 2012 the Yield on 30 year T Bond hit a low of 2.45% and the Bond price simultaneously hit its all-time high. Even in the dark days of December 2008 the yield on the 30 year bond reached a low of only 2.53% on the 18th of that month.

Over the last year the yield on the long bond has risen by 53% from 2.45% to 3.75%. On its own this reduced the Dividend Discount Value over the same period by 35% from 32,604 to 21.279. However, this was partially offset by a 9% increase in the dividend from $336.04 to $367.70. The net result, the Value has fallen by 27% to 23,337.

It might be noted that over the same period earnings rose by a mere 1.6% for $919.10 to $933.99.

While the Value has fallen over the past year the Price of the DJII has risen by 23% from 12,700 to 15,628 as there has gradually been a fading of fear and a partial restoration in the equilibrium between Price and Value. This should continue with the bias being upward pressure on Price since the Fed seems determined to keep long term rates under control and dividends should continue to rise. This and further improvement of investor sentiment as positive economic news unfolds should result in the DJII rising throughout the remainder of this year and well into next.

What about using earnings and P/E multiples?

Many commentators concentrate on earnings and P/E multiples but as shown, earnings have been extremely volatile during recessions.

It might also be noted that earnings have remain fairly static for the past couple of years suggesting that too much emphasis is placed on earnings in valuing equities.

As shown below, the P/E multiple has been even more volatile. Using an average P/E multiple in isolation, as a determinant of value is of little use, for it fails to consider the returns available from alternative investments such as the yield on the 30 year T Bond.

The Fed model suggests that the earnings yield (the reciprocal of the P/E multiple) should equal the long bond yield. However, with the volatility of earnings over time the fit, at a correlation of 0.36, is not the best as shown below. Despite this, it is important to note that before Lehman the earnings yield was rarely in excess of the long-bond yield to the extent that it has been over the last three and a half years. This also points to the persistence of "Irrational Pessimism", among market participants.

Assuming that the earnings yield returns to parity with the long bond yield then either interest rates have to rise or earnings drop or, as appears to be happening, the price of the DJII has to rise to 25,324. While this is higher than the value indicated by the Dividend Discount Model it should be remembered that the dividend payout ratio is historically low. Even so, the rise in the price of the DJII to match the Fed value is a similar order of magnitude to that using the Dividend Discount approach.

Data Sources: US Federal Reserve, Dow Jones.

Source: Dow Price Remains At A Huge Discount To Its Value - Buy (And Take No Prisoners)