windy anabasis

The Odd Arithmetic of Brad DeLong


Brad DeLong argues that investors can now expect a 7% return on their investment if they only dive into the SP500. Elsewhere, he argues that the equity risk premium is now 9%.

Let’s take a look.

I can buy shares in the SP500 and earn a whopping (annualized) dividend of 2%. Not 7%. After 90 days, I can sell my shares, absorbing any capital losses or gains. I compare that to holding a T Bill for 90 days, earning 0.

For the risk premium to be 9%, that means the expected capital gain (annualized) on a 90 day hold of the SP 500 needs to be 7%. I wonder why Brad DeLong believes, with a dividend yield of only 2%, that investors will bid up equities by 7% over the next year.

those relying on cap gains have not been doing well

Don’t compare earnings to coupons

I think one problem is the assumption implicit in the Fed Model that investors can take delivery of earnings. They cannot. They can only take delivery of dividends and capital gains. Firms must constantly re-invest merely to maintain their market power — this is a separate issue from replacement of depreciated capital. Intel must continuously build new billion dollar chip fabs not because the old fabs have depreciated away, but because the old fabs are no longer economically competitive, and so their market value to Intel (and to investors) goes to zero much faster than their IRS approved depreciation rates, or than their BLS depreciation rates marked in terms ability to produce chips. The investments that firms make are highly speculative — HP spent a billion to buy WebOS, and invested another billion, after which they decided that WebOS was not competitive and shut down the project. Microsoft spends billions on R&D not to grow its earnings, but to maintain them, as no one is going to be buying the previous model OS or Xbox. Verizon must invest in new infrastructure to maintain its competitive position vis-a-vis AT&T. Then it must make additional investments to grow its market share and increase its revenues and earnings. Monopolistically competitive firms must constantly re-invest to create new products simply to maintain their market power.

Current firms are less profitable per dollar of dividend paid

Investors only take delivery of dividends and capital gains. Whether or not earnings benefit investors is determined by the change in market cap of the firm, it is not determined by the dollar amount of investment made. Falling capital values means that even though firms continue to engage in speculative investment, the estimated long term profitability of the in place capital stock is questioned. Adobe, sitting on cash-flow pigs known as Photoshop and Illustrator has never paid out a dividend. Rather, it rolled those profits over into the acquisition of unprofitable ventures. The result was a decline of Adobe’s market cap even as Adobe earnings increased.

..but they have higher earnings per dollar of dividend paid

An earning statement cannot be assumed equivalent to a coupon payment — to do so understates the risk of holding equities and overstates the equity risk premium.

Allow for bubbles

Although one can imagine that over long periods, the dollar amounts spent on re-investment do correspond proportionally to an increase in the profit earning potential of the firm, this does not happen automatically, rather it happens due to a series of adjustments. The market must tell Adobe, “No, your re-investment is not competitive” by discounting the market value of its stock. As it does so, this does not mean that investors are more intolerant or risk-averse. It means that they are signaling to the market that they do not believe an additional dollar re-invested by the firm will earn the same return as the firm is currently earning. These adjustment periods do not happen continuously, or instantly, but take many decades. We have recently been in a house price bubble, during which time the rental yield on housing fell to a historic low of about 3%. It is now closer to the long run average, around 5%. That increase from 3% to 5% does not correspond to an increase in risk premium. Rather, during the bubble, investors believed that they were getting a yield of 3% plus capital gains. Now, without the capital gains (and possibly expecting capital losses), they demand a higher rental yield. Their total risk tolerance may not have changed, even though the apparent yield demanded increased. The price that someone is willing to pay for rental property if they expect no appreciation is different from the price that they are willing to pay if they expect appreciation.

Don’t Ignore Duration

The Fed model is the comparison of 10 year bonds with equity returns. Using the yield to maturity of the 10 year is problematic, as it assumes constant re-investment rates of the coupon, but holders of the 10 year bond will also experience capital gains over the course of their hold, and as they do so, they will not take delivery of the YTM return.

We can get rid of this problem by comparing SP 500 returns to 3 month T bill returns, assuming that the SP 500 shares are held for 90 days and then sold. Everyone has the choice of sitting on cash-equivalents for 90 days or jumping into the market. They do not have the option of obtaining the YTM yield on the 10 year if yields are changing.

The difference between the dividend + capital gain from holding equities over the 3 month period and the return on the 3 month bill measures the equity risk premium that investors demand for exposing themselves to the volatility of capital values over that 90 day period. The following graph plots the 5 YR forward and trailing SMA of this premium:

since the mid 1990s, ex-post and ex-ante risk premiums have been below average

The first thing to note is that at least ex-post, equity investors have taken a horrible beating, even as DeLong has repeatedly bemoaned their risk intolerance.

Even though the average value (over the 70 year period) of the equity premium has been 7.14%, recent values have been negative. Investors would have been better off buying the T-Bills.

There is no empirical basis to believe that investors are currently demanding a high risk premium. Not with dividend yields at 2%, and the real market cap of the SP500 in a secular decline. Rather, we see a situation similar to the 1970s, in which equity investors were routinely beaten with below average returns and above average volatility. That era was only brought to an end with rapidly falling (nominal) risk free rates, something not possible now. In the period of the 1940s, nominal rates were low but dividend yields were high, so there was reason to expect increasing capital gains if yields fell. With dividends at record lows, it is hard to imagine large capital gains. With no gain, the equity risk premium will be 2%, far below the 7% historical norm.

The problem here is that with a nominal dividend yield so low, the duration of the stock starts to explode. At 2%, the duration is over 50 years; it is misleading to compare stocks to the current 10 Year bond. Assuming that we exit this crisis before then (and that rates rise), investors are being asked to absorb capital losses when interest rates go up. Low nominal rates increase duration and make investors more far-sighted, and therefore less response to the special circumstances of the present. They care less about the present 2% spread between dividends and 0% T-bills, and more about the future spread between dividends and 4% T-Bills. The more the central bank rushes to lower rates to address the current crisis, the more far-sighted investors become, and the less concerned they are about the current low rates.  Therefore maintaining even the current market cap at a 2% yield is a sign of enormous patience and risk tolerance on the part of investors — the situation is completely different than if the short rate was at 5% and dividend yields were at 7%. Then we could be talking about high levels of risk premium.

In a situation with low dividend yields and zero risk-free rates, what would drive the rapid increase in capital gains necessary to justify the historical 7% equity premium that DeLong believes investors have. The equity premium is currently much lower, and the prospects for equities are more grim. Rather, we are in a period of both low equity risk premiums and falling capital values. Investors are both skeptical of the sustained profitability of current firm re-investment plans and they are willing to accept historically low yields if those yields are believed to be sustainable.

The only thing that equity investors have not been doing is obtaining total returns in excess of those holding  10 year bonds.