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There is a lot of discussion about how the end of the Federal Reserve's quantitative easing will affect the stock market. There are two schools of thought in this regard – the pessimists (the theoreticians) and the optimists (the empiricists).

The former argue that the rise in interest rates as a result of QE's end will be bad for stocks. They base their analysis on the theoretical relationship between interest rates and the present value of cash flows, which are key determinants of stock prices.

The optimists argue the opposite based on history. They point out that a bull market followed the bottoming of interest rates in 1941 – in fact, stock markets rallied for the following 20 years. Similarly, the optimists refer to the experience from the 1890s when interest rates started to rise but stock markets began a bull market that ended only in 1929.

There are a couple of problems with these arguments as they apply to the current market. Let me explain.

First of all, current interest rates are not theoretically correct but have been kept artificially low by policy makers. Artificially low interest rates lead to artificially high stock prices.

This has never been the case before. Had interest rates been determined by market forces and reached an equilibrium based on market conditions, stock prices would have been correct, reflecting fundamental values. This is not the case now.

As a result, when interest rates start to rise to more normal levels based on demand and supply conditions that reflect fundamentals, we may see a correction in stock prices. After the initial correction, the direction of stock prices will again be based on fundamentals.

However, having said that, we should consider the impact of QE on the yield curve – the line that depicts the relationship between short-term and long-term government bond yields. A positively sloped yield curve is one where short-term interest rates are lower than long-term rates. QE has tended to push down the rate on longer maturities, making the yield curve less positively sloped than it otherwise would be. An end to QE may result in a more positive slope to the curve.

There is evidence to suggest that positively sloped yield curves are good for the economy and for the stock market. A positively sloped yield curve indicates that markets expect rising interest rates in the future because of an improving economy. The steeper the yield curve, the better conditions are expected to be, which, in theory, is good for the stock market.

Positively sloped yield curves also give incentives to banks to lend, as it is more profitable for them to do so by borrowing short and lending long. And credit that is readily available helps economic expansions. So there may be some offset to the previously stated effect.

In addition, a rise in interest rates may not necessarily be bad for stock markets as long as economic growth conditions are such that interest-rate increases are lower than the increase in the rate of profit growth.

The argument goes that investors' expectations for the return they can reasonably expect to earn is usually tied to the current level of interest rates. As interest rates rise, so does the expected return. This, in turn, pushes down the price that investors are willing to pay for a dollar in earnings – the so-called price-to-earnings multiple, or P/E. As the P/E multiple declines, so do share prices.

However, this argument ignores the growth rate effect in the valuation model. In the long run, based on the equity valuation model with constant growth to infinity, the true rate to discount future corporate profits is not just the expected rate of return, but rather the expected rate of return less the growth rate in profits.

Will corporate profits increase fast enough to compensate for the rise in interest rates? Historically, the rise in interest rates coincided with sharply improving economic conditions and growth rates. Nowadays, the chances of fast economic growth are hampered by the many imbalances in the system.

Corporate profits are booming because of declining commodity prices and a weak jobs market that has driven down the cost of labour (the share of U.S. GDP going to labour income is at its lowest level in 50 years) so one has to wonder where the growth in profits will come from.

As a result, despite the historical evidence that bull markets coincide with rising interest rates, a rise in interest rates in the current environment may not be followed by a bull market.

In fact, it could turn out to be the opposite, assuming growth rates do not follow the rise in interest rates.

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