The concept that stock prices and interest rates enjoy an inverse relationship is actually quite theoretical rather than absolute. An inverse relationship seems to exist between stock prices and interest rates because interest rates are closely tied to discount rates, therefore a rise in interest rates do (frequently, but not always) have a negative impact on stock prices (and vice-versa). The strange relationship between stocks and interest rates is explained this way:

In an ideal world, the price of a stock would equal to the present value (PV) derived from adding up the expected dividends from each year in the stock's future.

Because of expected future impact, when interest rate rises by a certain percentage, a stock's price (in present value) drops by more than that percentage. Thus, stock prices and interest rates have an inverse relationship.

Put simply, a $20 dividend paying stock in a 10% economy is valued the same as a $50 dividend paying stock in a 25% economy. When interest rates increase we can reasonably expect stocks to drop in price.

The reason for this happening is quite simple. When a person invests in the stock market, he expects a certain level of return. Now, when the interest rate rises, the price at which he buys the stock needs to be low enough for him to benefit from the increased interest rate. If the price of the stock were to fall rather than rise, the additional benefit that he may derive from a higher interest rate will be negated by the higher cost of the stock.

The required return might rise if the risk premium or the risk-free rate increases. For instance, the risk premium might go up for a company if one of its top managers resigns or if the company suddenly decides to lower its dividend payments. And the risk-free rate will increase if interest rates rise.

So, changes in interest rates impact the theoretical value of companies and their shares: basically, a share's fair value is its projected future cash flows discounted to the present, using the investor's required rate of return. If interest rates fall and everything else is held constant, share value should rise. It is for this reason that a cut in interest rates by a central bank is greated with cheers from the market. This is particularly so of the lowering of interest rates by the United States Federal Reserve. Because the interest rates in the U.S have a chain effect around the world, a rise or cut in U.S interest rates greatly affects global markets.

If interest rates drop then money is cheaper (this is because people or businesses can borrow money at a lower cost, from banks).

In turn this leads to

More money invested in the stock market, which drives up the demand for stocks.

There are fewer new issues of stocks because businesses prefer to borrow money at a cheaper rate from banks, rather than from investors.

With key short-term interest rates increasing, a large part of the funds could be siphoned off to the bond and debt markets or vice versa.

The graph below traces the nexus between interest rates and returns generated by the debt market.

This above mentioned graph shows the fluctuations in the interest rates spanning the duration of 8 years in three different regions which comprises of huge chunk of the debt market.

Now through this chart we can infer that due to inflationary tendencies and because of other market forces, the lending rate is passes through ups and downs.

At the same point of time, to ease the pressure on equity market, lending rates have gone down in this span so as to spurt the inverse relationship between interest rate and equity returns.

Again in graph above we can see that debt markets were volatile in this span due to easening of interest rates in the same span of time which showcased the downfall in debt returns of U.S. aggregate index for debt market as compare to the returns generated by equity market.

There is a rise in equity returns in these two different time slots shown in the graph above. This is because interest rates have plummeted to attract more inflows in the domestic market which in turn led to a rise in equity returns.

Alignment of Indian & Global Rates:

Thanks to increasing levels of globalization, in the Indian economy interest rates are getting aligned with the global interest rates. The RBI's stance has been to keep the Indian rates higher than that of the US and other G-7 countries in order to attract capital. Over the last two years, increase in the US and EU interest rates has been followed by increase in the domestic rates as well (See table).

To sum up, it is safe to say that interest rates have a mixed impact upon both forms of market, because it is not the only factor which rules the market. What is significant is that equity and debt returns share an inverse relation most of the time.