Friday, August 16, 2013

Some Simple Math Suggests that Increasing Bond Yields Have Reduced the Fair Value of Stocks by 30%

With bond yields spiking to 2 year highs thanks to mass selling by foreign investors (and I'm sure plenty of US ones as well) a simple exercise in terms of what higher yields do to equity valuations is probably in order.  Check out Brett Arends' very interesting piece in which simple math suggests that fair value for the stock market has just been reduced by 30%.  And if yields normalize to their long term level of 4.5%, fair value will be reduced by 50%:

Imagine a share of stock that will pay you $100 in dividends every year for the next, say, 100 years. How much is that worth in today's money? How much would you pay for that stock? To know the value, you have to apply a relevant "discount rate" — in layman's terms, and with some oversimplification, you have to know what interest rate you could get on the money if you didn't buy the stock.

In May, you knew you could earn 1.6% a year, at least for the next 10 years, if you left your money in ten-year Treasury notes. Applying a 1.6% discount rate to our stream of $100 dividends produces a value of $4,972. In other words, that's how much that theoretical stock would be worth, in today's money, if we use a discount rate of 1.6%.

Hike that discount rate to 2.7% — the interest rate on the Treasury note today — and that value collapses by nearly a third, to $3,445. Hike the discount rate to 4.5% — a normal rate on the Treasury — and the value halves to $2,240.

To put this in very simple logic: The Federal Reserve has been suppressing interest-rates to boost the economy. That suppression artificially hiked the value of the stock market, by a simple mathematical equation. Now that suppression is coming to an end, interest rates can be expected to rise. That rise ought — again, by a simple mathematical equation — to reduce the value of the stock market. Dramatically.

You can play with the numbers. I've applied different discount rates, adding in an 'equity risk premium' for the extra return stock-market investors want to earn above risk-free Treasury bonds. I've assumed the stream of dividends will grow year after year. None of that changes the direction of the math. (Indeed, if we assume dividends will rise over time, which seems reasonable, the math gets even worse — higher interest rates reduce the valuations by even greater amounts). Taking the ten-year Treasury rate from May's 1.6% to a "normal" 4.5% adds about three percentage points to the discount rate. Mathematically, that can slash the valuation of the stock market by 30% to 50% under basic financial calculations.

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