Confusing "yields" in the bond market

Now retail investors can invest in G-Secs and T-bills. Personally, I feel it is a win-win situation and a very important market gap being filled. Until now if we needed to invest in these securities, we had to go through mutual funds as individual investors. But opening up for retail investors will be beneficial to both the government and individuals. 

I say this because I feel G-Secs are very secure assets and rather than keeping excess amount in banks or un-necessarily investing in market risk equities, it is far better to go into G-Secs. Yes, they can be tapped through mutual funds but then they have their own fee and they are subjected to market risks as well and have their own complications. However, being personally being able to invest, I would suggest everyone allocate a fraction of their portfolios to this instrument. The fraction depends on the investment horizon and risk appetite. But especially to people nearing retirement, rather than going into other instruments, seriously consider this. Even in the banks, by RBI only money up to 1 lakh is insured. So, beyond that, we are actually taking a risk. Having said that one must maintain liquidity via their bank account but the excess should be allotted to G-Secs. These are safe instruments as they come with Government of India backing. 

These instruments would also help access the additional savings in the hands of retail investors to raise money. I think this is very smart and a beneficial move for the government as well. For more details visit the following links: [1], [2]

Having said that, there are few things which confuse me about the bond-market which I wanted to discuss here. For details about fixed-income securities and bond market, you may refer to my notes titled "Understanding Financial Markets".

1. The current yield of the bond is the annual income associated with it in the form of coupon payments and its current price. It is the ratio of annual cash flows and market price. So, this tells the investor about the return they can expect if they purchase the bond and hold it for one year. For example, if the investor buys 5% coupon rate (annual-rate) bond for a discount of $900, that means that annually the investor would receive $50. The current yield would then be, 50/900 or 5.56%. Note that if the price of the bond were $1000, then the current yield would equal the coupon rate. Also, note that this method doesn't account for the additional cash flow that we will have if we buy the bond and let it mature, that is, the difference between the price of the bond and the face value.

2. Coupon yield is the annual interest rate established by the issuer when the bond is issued. It remains fixed for the entirety of bond until its maturity. It is expressed as a percent of bonds face value.

3. Yield to maturity (YTM) differs from the coupon rate but is an important metric. The YTM of the bond is essentially the internal rate of return (IRR) associated with buying that bond and holding it until its maturity date. YTM is also called a book yield or redemption yield. So this is similar to the current yield in the sense that it also determines how much money one would make by buying the bond and holding for a year. However, unlike current yield, it takes a present value (PV) into consideration. In this way, it accounts for the time value of money where the current yield does not. In addition, unlike the current yield which takes coupons in the simple interest way, YTM assumes that the coupon is re-invested in some security (not necessarily this bond) but which yields the same return as is earned on this bond or the coupon rate. So it compounds.

Mathematically, the YTM can be understood in the following way,

So, knowing the price of the bond, coupon value and face value of the bond, we can calculate its YTM. Since the relationship is non-linear, it might be difficult to obtain an analytical solution. 

Let's take another example to understand current yield and YTM difference. Suppose there's $1000 bond with a 5% coupon rate (annualized rate) with semi-annual coupon payment frequency (6 monthly) and matures in 30 years. The simple interest way would suggest the gain $1500 dollars after 30 years. However, with YTM, that is, compound interest way, we get gain of $3400 after 30 years. Now, as in the previous example, if we had bought the bond at $900, simple interest way wouldn't account for the difference in cash flow if we hold it until maturity, here $100 gain. But, YTM does account for all such cash-flows and so is more comprehensive. 

Another important point to note here is that the bond price effects the YTM. Use the calculator here and test [3]. Continuing on the previous example, if the same bond were traded at a discount of $900, YTM comes out to be greater 5.61% (> coupon rate), if the bond were traded at $1000 then YTM comes out to be 5% (= coupon rate) and if the bond were traded at a premium of $1100, YTM comes out to be 4.39% (< coupon rate).

Apart from the yield aspect, another important parameter in the bond market is that of duration. Duration determines the sensitivity of the price of the bond to change in interest rates. We can think of duration as the time period (in years) it would take for an investor to be repaid the bond's price through receipt of bonds total cash flows (coupons+initial amount at maturity). In most bond-searching and analysis tools, the duration is measured by the Macaulay duration method. This method finds the present value of bonds future payments and their maturity levels. 

Mathematically it can be understood in this way,