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Implied Dividend Method for Modeling Effects of Rate Changes on Stock Prices

This article is my study on whether I could model stock prices changes when the risk free rate chages. The followings are the setup of this study:

  • Stock valuation is based on the dividend discount model (DDM).
  • The stock pays quarterly dividends.
  • The risk free rate is constant for all investment time horizon.
  • I frist assume a annual risk free rate which is divided by 4 to get quarterly rate that matches the divided paying date for stock pricing based on DDM.
  • The stock price is the real trading price which is used in DDM to get implied dividend amounts.
  • Stock pays constant dividends. They don't increase or decrease.
  • Apply DDM again with a different annual rate and the implied dividends to get new stock price.

APP

Current Stock Price: $
Current Annual Rate: %
Change in Rate: %

Rate of Stock Price Change at Different Yield

We see the lower the yield, the greater its change has an impact on the stock price.
Yield Stock Price Price Change
1% $4000 NA
2% $2000 -50%
3% $1333.33 -33.33%
4% $1000 -25%
5% $800 -20%

Then we take the first derivitive with respect to rate to find the rate of change in stock price when yield changes.
df/dr = -dividends / (r^2)

Scenario Analysis

2022 Fed's Rate Hikes

The S&P reached its high on Jan 04, 2022 at 4,793.54 points. On Jan 03, 2022, the US 10-year yield was 1.715%.

If I apply the above data into my app, a rate hike of 0.75% would bring down the stock price 30.43%. 

The US 10-year treasury yield as I am writing this article is about 3%, the S&P 500 index is 3959.90, and the Fed is said to hike rate 0.75%.

Applying these data, I got a decrease of 20% in stock price.

Conclusion

The stock price moves dramatically with the change of yield. This I'd because this method does not consider dividend growth which could be a proxy for business growth. Taking into account the growth rate of dividend, the DDM Formula becomes dividends divided by rate minus the growth rate. If the growth rate is relatively big, rate change will have less impacts on the stock price.
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