 Personal Finance PowerPoint Presentation, Bond Yield. Prepare to get financially fit by practicing personal finance. Most of this information comes from Investopedia Bond Yield, which you can find online. Take a look at the references, resources, continue your research from there. This by Adam Hayes updated January 1st, 2022. In prior presentations, we've been looking at investment goals, investment strategies, investment tools, keeping them in mind. We're now asking, what is Bond Yield? Bond Yield is the return an investor realizes on a bond. The Bond Yield can be defined in different ways. Setting the Bond Yield equal to its coupon rate is the simplest definition. So when we're thinking about investing, we typically want that diversified portfolio, possibly having some investments in stocks or equities, some in the fixed income, possibly then bonds. We can think of bonds as, in essence, basically loaning money to the issuer of the bond, that being either the government or a corporate type of bond. The stream of many typical bonds will be that if we look at future cash flows of the bond, we're usually going to get some kind of interest on a fixed proportion, possibly semi-annually, oftentimes for the bond. That's kind of like the rent on the money that we, in essence, loaned to the issuer, government or corporation. And then we get the face amount, basically the return, basically, at the end of the bond. So we've got these two kind of ways that we get paid back. In other words, we're not getting paid back like a loan that we might get if we were to get a mortgage in installment payments that have a bit of principle and interest related to them. Oftentimes, we have the interest in and of itself. And then, in essence, basically the principle at the maturity of the bond. So we want to figure out what the yield is, basically what our return is on the bond and possibly use that in order to make estimates and value different bonds and think about what the best investment strategy would be upon them. So the current yield is a function of the bond's price and its coupon or interest payment, which will be more accurate than the coupon yield if the price of the bond is different than its face value. So if you're looking at bonds that just got issued, then it could be the case that, in essence, the market price is basically the same as the face value or the market rate would be the same as the rate, basically, on the bond. But as time passes, if a bond has been issued, especially if you're going to be purchasing it, say, on the secondary market, rather than from the issuer, then there could be changes with regards to what people expect market rates versus the rate that is on the bond. Now, normally, if you were looking at a loan situation, when you look at a loan, you basically adjust the interest rate to whatever the current interest rate is oftentimes. But if you're looking at a bond which has the interest rate already on it and has the face amount on it, then you're going to have to adjust the price to account for the fact that now the market has changed. There's different rates on the market, which means you're going to be purchasing it at a discount, something less than the face value of the bond or a premium, something more than the face value of the bond. So more complex calculations of a bond's yield will account for the time value of money and compounding interest payments. So basically, when we try to figure out what the proper account will be, we typically want to think about it in terms of a stream of payments, which we just said has two streams of payments, typically the interest stream and then the stream at the end with regards to the face amount at the end and consider our time value of money calculations. We might do some examples on this to understand it a little bit more in future presentations. So these calculations include yield to maturity. That's the YTM bond equivalent yield, B-E-Y, and effective annual yield, E-A-Y. So overview of bonds yield. When investors buy bonds, they essentially lend money to issuers money. So they're lending money to the issuer corporation or the government. In return, bond issuers agree to pay investors interest on bonds through the life of the bond and to repay the face value of bond upon maturity. So the simplest way to calculate a bond yield is to divide its coupon payment by the face value of the bond. This is called the coupon rate. So you're just going to take the annual coupon payment, which is basically the interest payment. Typically, we're looking at an annual payment here for the year and then divide it by the bond face value. So that would be the simplest kind of calculation. If a bond has a face value of $1,000 and made interest or coupon payments of 100 per year, then its coupon rate is 10%. It's going to be the 100 divided by 1,000 or the 10%. However, sometimes a bond is purchased for more than its face value premium or less than its face value discount, which will change the yield an investor earns on the bond. So this will often happen if you buy, say, in the secondary market, for example. So bond yield versus price. As bond prices increase, bond yields fall. For example, assume an investor purchased a bond that matures in five years with a 10% annual coupon rate and a face value of $1,000. Each year, the bond pays 10% or $100 in interest. Its coupon rate is the interest divided by its par value. If interest rates rise above 10%, the bond's price will fall if the investor decides to sell it. So in other words, what does that mean if interest rates go above 10%? It doesn't mean the rate on the bond is going to go up by 10%. It's stuck at the 10%, which was what the rate was when they issued the bond. It means that if market rates go up, meaning people are demanding rates of an equivalent kind of bond at a higher rate than it was when the bond was issued, that's what they're talking about. So the bond's price will fall because people could buy other bonds and get a higher rate on the newer bonds that are out there. Therefore, if you want to sell the bond at the 10%, you're going to have to sell. You're going to have to adjust the price for it because you can't adjust the interest rate. So for example, imagine interest rates for similar investments rise to 12.5%. The original bond still only makes a coupon payment of $100, which would be unattractive to investors who can buy bonds that pay $125 now that interest rates are higher. So how are you going to offload your bond when it only pays $100 and they can get other ones for $125? You can adjust the price. So if the original bond owner wants to sell the bond, the price can be lowered so that the coupon payments and maturity value equal a yield of 12%. So they're not going to adjust the interest payments that you're going to get, but instead adjust, it might be 12.5%, but instead adjust the price. So in this case, that means the investor would drop the price of the bond to $927.90. Now that calculation, you can see it in theory why you would drop the price, but getting exactly to that $9.27.90 would reduce some time value of money kind of calculations. We might do that in some example problems, but you get the idea. So in order to fully understand why this is the value of the bond, you need to understand a little more about how the time value of money is used in bond pricing, which is discussed later, so we'll take a look at it shortly. So if interest rates were to fall in value, the bond's price would rise because its coupon payment is more attractive. So if, on the other hand, we've got a rate on the bond at 10%, and now the market has market rates that are lower for current bonds being issued, well, now your bond looks good because you're getting more money than other people are getting. So for example, if interest rate falls to 7.5% on the market, not on the bond, the similar investments, the bonds seller could sell the bond for $1,101.15. Now again, you get the idea that you could sell it for over $1,000. Where do they get that $1,101.15? That's kind of, we got to do the time value of money thing, but you get the idea of which way it's going to go, premium discount, so on. So the further rates fall, the higher the bond's price will rise, and the same is true in reverse when interest rates rise. So in another, let me read that again. The further rates fall, the higher the bond's price will rise, and the same is true in reverse when interest rates rise. In other scenario, the coupon rate no longer has any meaning for a new investor. However, if the annual coupon payment is divided by the bond's price, the investor can calculate the current yield and get a rough estimate of the bond's true value. So current yield, annual coupon payment divided by the bond price. So the current yield and the coupon rate are incomplete calculations for a bond's yield because they do not account for the time value of money, maturity value, or payment frequency. So it's a little too easy to do that calculation. That's kind of a rough calculation that you can use because you're not taking into account the time value of money and the fact that you got these two kind of streams of future cash flow, the interest payments, and then the principal at the maturity. More complex calculations are needed to see the full picture of the bond's yield. So we got the yield to maturity. A bond's yield to maturity, the YTM, is equal to the interest rate that makes the present value of all a bond's future cash flows equal to its current price. So if you're kind of figuring the price in essence or what the price, you would do this calculation to try to figure out the cash flows of all the future cash flows. Now you might do this in Excel as well. You could do this with a formula. Sometimes it's easier to do in Excel. You could have a financial calculator to do. We'll try to show it pictorially in some example problems. So these cash flows include all the coupon payments and its maturity value. Solving for the YTM is a trial and error process that can be done on a financial calculator, but the formula is as follows. So we'll do some examples in Excel on it. In the previous example, a bond with a $1,000 face value, five years to maturity and 100 annual coupon payments was worth $927.90 in order to match a year to date, a year to date, I'm sorry, yield to maturity YTM of 12%. So in that case, the five coupon payments and the $1,000 maturity value were the bond's cash flow. Finding the present value of each of those six cash flows with a discount or interest rate of 12% will determine what the bond's current price should be. Bond equivalent yield, this is the BEY. Bond equivalent yields are normally quoted as a bond equivalent yield BEY, which makes an adjustment for the fact that most bonds pay their annual coupon in two semi-annual payments. So now you got these two payments that you're really dealing with with the bonds because they pay semi-annually instead of yearly typically. In the previous example, the bond's cash flows were annual, so the YTM is equal to the BEY. However, if the coupon payments were made every six months, the semi-annual YTM would be 5.979. The BEY is a simple annualized version of the semi-annual YTM and is calculated by multiplying the YTM by two. So in this example, the BEY of a bond that pays semi-annual coupon payments of $50 would be 11.958, which is the 5.979 times two to get that amount. The BEY does not account for the time value of money for the adjustment from a semi-annual YTM to an annual rate. So effective annual yield, the EAY. Investors can find a more precise annual yield once they know the BEY for a bond if they account for the time value of money in the calculation. In the case of a semi-annual coupon payment, the effective annual yield EAY would be calculated as follows. We got the formula down below. So if an investor knows that the semi-annual YTM was 5.979, they could use the previous formula to find the EAY of 12.32. Because the extra compounding period is included, the EAY will be higher than the BEY. Complications finding a bond's yield. There are a few factors that can make finding a bond's yield more complicated. For instance, in the previous example, it was assumed that the bond had exactly five years left to maturity when it was sold, which would rarely be the case because it's an exact whole years that we have here. So when calculating a bond's yield, the fractional periods can be dealt with simply. The accrued interest is more difficult. For example, imagine a bond that has four years and eight months left to maturity instead of that last full year. The exponent in the yield calculation can be turned into a decimal to adjust for the partial year. However, this means that four months and the current coupon period have elapsed and there are two more to go, which requires an adjustment for accrued interest. A new bond buyer will be paid the full coupon. So when you get the full coupon, if you have the bond at that point in time, even though you haven't had it for the whole six months, if it was a semi-annual coupon. So the bond's price will be inflated slightly to compensate the seller for the four months and the current coupon period that have elapsed. Bonds can be quoted with a clear clean price that excludes the accrued interest or the dirty price that includes the amount owed to reconcile the accrued interest. When bonds are quoted in a system like a Bloomberg or a Reuters terminal, the clean price is used. What does a bond's yield tell investors? A bond's yield is a return to an investor from the bond's coupon interest payment. It can be calculated as a simple coupon yield, which ignores the time value of money. Any changes in the bond's price are using a more complex method like yield to maturity. Higher yields mean that bond investors are owed larger interest payments, but may also be a sign of greater risk. The riskier a borrower is, the more yield investors demand to hold their debt. Higher yields are also associated with longer maturity bonds. Are high yield bonds better investments than low yield bonds? Like any investment, it depends on one's individual circumstances, goals, and risk tolerance. Low yield bonds may be better for investors who want a virtually risk-free asset or one who is hedging a mixed portfolio by keeping a portion of it in low-risk assets. High yield bonds may instead be better suited for investors who are willing to accept a degree of risk and return for a higher return. The risk is that the company or government issuing the bond will default on its debts. A diversification can help lower portfolio risk while boosting expected returns. What are some of the common yield calculations? The yield to maturity YTM is the total return anticipated on a bond if the bond is held until its maturity. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. YTM, yield to maturity, is usually quoted as a bond equivalent yield, BEY, which makes bonds with coupon payment periods less than a year easy to compare. The annual percentage yield, APY, is the real rate of return earned on a savings deposit or investment taking into account the effect of compounding interest. The annual percentage rate APR includes any fees or additional costs associated with the transaction, but it does not take into account the compounding of interest within a specific year. An investor in a callable bond also wants to estimate the yield to call, the YTC, or the total return that will be received if the bond purchased is held only until its call date instead of the full maturity. So that's when you've got that option that it could be called at some point in time. So now you've got this kind of complexity of the maturity date versus the date that it could be called. So how do investors utilize bond yields? In addition to evaluating expected cash flows from individual bonds, yields are issued for a more sophisticated analysis. Traders may buy and sell bonds of different maturities to take advantage of the yield curve, which plots the interest rates of bonds having equal credit quality but differing maturity dates. The slope of the yield curve gives an idea of future interest rate changes and economic activity. They may also look at the difference in interest rates between different categories of bonds holding some characteristics constant. A yield spread is the difference between the yields on differing debt, instruments of varying maturities, credit ratings, issuer or risk level calculated by deducting the yield on one instrument from the other. For example, the spread between AAA corporate bonds and US Treasuries. The difference is most often expressed in basis points, BPS, or percentage points. Thank you.