relationship between equity markets and bond yield

Bond yields are the key to calculating opportunity cost of equities 
Bond yields, in a way, represent the opportunity cost of investing in equities. For example, if the 10 year bond is yielding 7 % per annum then the equity markets will be attractive only if it can earn well above 7 %. In fact, equity being risky there will have to be a risk premium, first of all, to be even comparable. Let us assume that the risk premium on equities is 5 %. Therefore that 12 % will literally act as the opportunity cost for equity. Below 12 %, it does not make sense for the investor to take the risk of investing in equities as even the additional risk is not being compensated. The question of wealth creation only begins after that. As bond yields go up the opportunity cost of investing in equities goes up and therefore equities become less attractive. That is the first reason that explains the negative relationship between bond yields and equity markets. 
Bond yields are normally compared with earnings yield 
Bond yields are normally compared to the earnings yield. The earnings yield is nothing but the EPS / price of the stock. It essentially tells you what the share is actually earning assuming that you enter at the current price. A stock is attractive only if the earnings yield is higher than the bond yield. Otherwise, why should one take the risk of taking in equities? However, this argument is not always applicable. It is not applicable in cases where the company is loss making and the investors are buying stocks on expectations of a turnaround in the stock performance. There is another way to look at this. Earnings yield is the reverse of the P/E ratio which is a valuation matrix. That means if the bond yields go up then equity investors expect to be able to buy the stock at lower P/E ratios. 
Bond yields impact the cost of capital in valuing equities 
This is a very important relationship and causal effect. The yield on bonds is normally used as the risk-free rate when calculating cost of capital. When bond yields go up then the cost of capital goes up. That means that future cash flows get discounted at a higher rate. This compresses the valuations of these stocks. That is one of the reasons that whenever the interest rates are cut by the RBI, it is positive for stocks. Normally stocks tend to get re-rated as they will now be valued based on a lower cost of capital discounting factor.
 Bond yields impact colour of Foreign Institutional flows
 This is a very interesting relationship we have seen in recent years. When the bond yields in India go up, global investors find Indian debt more attractive in relation to global debt. This leads to capital outflows from equities and inflows into debt. In the last few months, we have seen outflows from FIIs in equities, but debt has continued to attract interest due to attractive yields. Of course, the domestic funds have been large scale buyers in equity and they have supported markets but that is a different issue altogether. The crux is that FPIs look at Indian equity and debt as competing asset classes and allocate according to relative yields. 
Bond yields impact financial costs.. 
Bond yields are very important fundamental factor that sets the relationship between bond yields and equities. When bond yields go up, it is a signal that corporates will have to pay a higher interest cost on debt. As debt servicing cost goes higher, the risk of bankruptcy and default also increases and this typically makes mid-cap and highly leveraged companies vulnerable. Bond yields have been typically used by analysts and investor as an important lead indicator to gauge the direction of equities. More often than not, it works to a T!

Q: There is another connection that is running between markets which is between the bond yield and equity markets. Explain why the equity market is so sensitive to the bond market yield? The moment the yield goes higher the market gets a bit nervous that is often seen as a negative for equity markets. How does that work actually?
A: There is clearly the relationship between equity markets and bond yield future returns are discounted using the 10 year bond yield as a discounting factor. And lower are your bond yields the better are the returns for the equity market and conversely in a high yield environment the future returns are much lower because bond yields are used to discount future returns. But intuitively that is just statistics, intuitively in a falling interest rate environment there is a direct impact on banks. Banks have some holding of government bonds in their portfolio therefore falling yield environment there are mark to market gains for banks on their holding of government bonds plus falling yields imply lower cost of borrowing for consumers and therefore higher potential that consumers are going to borrow more and spend more in the coming quarters.

Falling yields indicates that corporate borrowing costs are going to come down therefore companies are more likely to invest more in future project and therefore falling bond yields basically indicates that domestic demand is going to pick up in the coming quarters with better earnings are always positive for equity markets and therefore the positive relationship between falling bond yields and future equity returns. And yields of course are inversely proportional to prices therefore falling yields typically means that bond prices are going up.