## Bond Yields For Security Analysis And Portfolio Management MCOM Sem 3 Delhi University Notes

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### Bond Yields For Security Analysis And Portfolio Management MCOM Sem 3 Delhi University Notes

Bond Yields For Security Analysis And Portfolio Management MCOM Sem 3 Delhi University : A bond yield is the amount of return an investor realizes on a bond. Several types of bond yields exist, including nominal yield which is the interest paid divided by the face value of the bond, and current yield which equals annual earnings of the bond divided by its current market price. Additionally, required yield refers to the amount of yield a bond issuer must offer to attract investors.

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#### BREAKING DOWN ‘Bond Yield’

When investors buy bonds, they essentially lend bond issuers money. In return, bond issuers agree to pay investors interest on bonds throughout their lifetime and to repay the face value of bonds upon maturity. The money that investors earn is called yield. Investors do not have to hold bonds to maturity. Instead, they may sell them for a higher or lower price to other investors, and if an investor makes money on the sale of a bond, that is also part of its yield.

#### Bond Yield Versus Price

As bond prices increase, bond yields fall. For example, assume an investor purchases a bond with a 10% annual coupon rate and a par value of $1,000. Each year, the bond pays 10%, or $100, in interest. Its annual yield is the interest divided by its par value. As $100 divided by $1,000 is 10%, the bond’s nominal yield is 10%, the same as its coupon rate.

Eventually, the investor decides to sell the bond for $900. The new owner of the bond receives interest based on the face value of the bond, so he continues to receive $100 per year until the bond matures. However, because he only paid $900 for the bond, his rate of return is $100/$900 or 11.1%. If he sells the bond for a lower price, its yield increases again. However, if he sells for a higher price, its yield falls.

#### When Do Bond Yields Fall?

Generally, investors see bond yields fall when economic conditions push markets toward safer investments. Economic conditions that might decrease bond yields include high rates of unemployment and slow economic growth or recession. As interest rates increase, bond prices also tend to fall.

#### Interest Rates Versus Bond Prices

To examine the relationship between interest rates and bond prices, imagine an investor buys a bond from ABC Corporation with a 4% coupon rate and a $1,000 face value. Another investor waits a few weeks before buying a bond, and during that time, the issuer raises interest rates to 6%. At this point, the second investor can buy a $1,000 bond from ABC Corporation and receive $60 in interest per year.

Meanwhile, upset that he is only earning $40 per year, the original investor decides to sell, but to entice others to buy his bond instead of bonds directly from ABC Corporation, he lowers his price. For example, he lowers it to $650, making its effective annual yield $40/$650 or 6.15%. If the bond issuer had not increased its rates, the investor might not have had to sell his bond for less than its face value.

### Bond Yields For Security Analysis And Portfolio Management Mcom Sem 3 Delhi University Notes

Bond Yields For Security Analysis And Portfolio Management MCOM Sem 3 Delhi University : A bond is a debt investment in which an investor loans money to an entity (typically corporate or governmental) which borrows the funds for a defined period of time at a variable or fixed interest rate. Bonds are used by companies, municipalities, states and sovereign governments to raise money and finance a variety of projects and activities. Owners of bonds are debtholders, or creditors, of the issuer.

### Bond Yields For Security Analysis And Portfolio Management Mcom Sem 3 Delhi University Notes

Bond Yields For Security Analysis And Portfolio Management MCOM Sem 3 Delhi University : The market prices bonds based on the bond’s particular characteristics. A bond’s price changes on a daily basis, just like that of any other publicly-traded security, where supply and demand in any given moment determines that observed price. But there is a logic to how bonds are valued. Up to this point, we’ve talked about bonds as if every investor holds them to maturity. It’s true that if you do this you’re guaranteed to get your principal back plus interest; however, a bond does not have to be held to maturity. At any time, a bondholder can sell their bonds in the open market, where the price can fluctuate, sometimes dramatically.

The price of a bond changes in response to changes in interest rates in the economy. This is due to the fact that for a fixed-rate bond, the issuer has promised to pay a coupon based on the face value of the bond – so for a $1,000 par, 10% annual coupon bond, the issuer will pay the bondholder $100 each year.

Say that prevailing interest rates are also 10% at the time that this bond is issued, as determined by the rate on a short-term government bond. An investor would be indifferent investing in the corporate bond or the government bond since both would return $100. Imagine a little while later, however, that the economy has taken a turn for the worse and interest rates drop to 5%. Now, the investor can only receive $50 from the government bond, but would still receive $100 from the corporate bond. This makes the corporate bond much more attractive, and so investors in the market will bid up the price of the bond until it trades at a premium that equalizes the prevailing interest rate environment – in this case the bond will trade at a price of $2,000 so that the $100 coupon represents 5%. Likewise, if interest rates soared to 15%, then an investor could make $150 from the government bond and would not pay $1,000 to earn just $100. This bond would be sold until it reached a price that equalized the yields, in this case to a price of $666.67.

This is why the famous statement that a bond’s price varies inversely with interest rates works. When interest rates go up, bond prices fall in order to have the effect of equalizing the interest rate on the bond with prevailing rates, and vice versa. Another way of illustrating this concept is to consider what the yield on our bond would be given a price change, instead of given an interest rate change. For example, if the price were to go down from $1,000 to $800, then the yield goes up to 12.5%. This happens because you are getting the same guaranteed $100 on an asset that is worth $800 ($100/$800). Conversely, if the bond goes up in price to $1,200, the yield shrinks to 8.33% ($100/$1,200).

The market prices bonds based on the bond’s particular characteristics. A bond’s price changes on a daily basis, just like that of any other publicly-traded security, where supply and demand in any given moment determines that observed price. But there is a logic to how bonds are valued. Up to this point, we’ve talked about bonds as if every investor holds them to maturity. It’s true that if you do this you’re guaranteed to get your principal back plus interest; however, a bond does not have to be held to maturity. At any time, a bondholder can sell their bonds in the open market, where the price can fluctuate, sometimes dramatically.

The price of a bond changes in response to changes in interest rates in the economy. This is due to the fact that for a fixed-rate bond, the issuer has promised to pay a coupon based on the face value of the bond – so for a $1,000 par, 10% annual coupon bond, the issuer will pay the bondholder $100 each year.

Say that prevailing interest rates are also 10% at the time that this bond is issued, as determined by the rate on a short-term government bond. An investor would be indifferent investing in the corporate bond or the government bond since both would return $100. Imagine a little while later, however, that the economy has taken a turn for the worse and interest rates drop to 5%. Now, the investor can only receive $50 from the government bond, but would still receive $100 from the corporate bond. This makes the corporate bond much more attractive, and so investors in the market will bid up the price of the bond until it trades at a premium that equalizes the prevailing interest rate environment – in this case the bond will trade at a price of $2,000 so that the $100 coupon represents 5%. Likewise, if interest rates soared to 15%, then an investor could make $150 from the government bond and would not pay $1,000 to earn just $100. This bond would be sold until it reached a price that equalized the yields, in this case to a price of $666.67.

This is why the famous statement that a bond’s price varies inversely with interest rates works. When interest rates go up, bond prices fall in order to have the effect of equalizing the interest rate on the bond with prevailing rates, and vice versa. Another way of illustrating this concept is to consider what the yield on our bond would be given a price change, instead of given an interest rate change. For example, if the price were to go down from $1,000 to $800, then the yield goes up to 12.5%. This happens because you are getting the same guaranteed $100 on an asset that is worth $800 ($100/$800). Conversely, if the bond goes up in price to $1,200, the yield shrinks to 8.33% ($100/$1,200).

The yield-to-maturity (YTM) of a bond is another way of considering a bond’s price. YTM is the total return anticipated on a bond if the bond is held until the end of its lifetime. Yield to maturity is considered a long-term bond yield, but is expressed as an annual rate. In other words, it is the internal rate of return of an investment in a bond if the investor holds the bond until maturity and if all payments are made as scheduled. YTM is a complex calculation but is quite useful as a concept evaluating the attractiveness of one bond relative to other bonds of different coupon and maturity in the market. The formula for YTM involves solving for the interest rate in the following equation, which is no easy task, and therefore most bond investors interested in YTM will use a computer:

We can also measure the anticipated changes in bond prices given a change in interest rates with a measure knows as the duration of a bond. Duration is expressed in units of number of years since it originally referred to zero-coupon bonds, whose duration *is* its maturity. For practical purposes, however, duration represents the price change in a bond given a 1% change in interest rates. We call this second, more practical definition the modified duration of a bond. Duration can be calculated to determine the price sensitivity to interest rate changes of a single bond, or for a portfolio of many bonds. In general, bonds with long maturities, and also bonds with low coupons have the greatest sensitivity to interest rate changes. A bond’s duration is not a linear risk measure, meaning that as prices and rates change, the duration itself changes, and convexity measures this relationship.

### Bond Yields For Security Analysis And Portfolio Management Mcom Sem 3 Delhi University Notes

Bond Yields For Security Analysis And Portfolio Management MCOM Sem 3 Delhi University : A bond is a debt instrument: it pays periodic interest payments based on the stated (coupon) rate and return the principal at the maturity.

Cash flows on a bond with no embedded options are fairly certain and the price of bond equals the present value of future interest payments plus the present value of the face value (which is returned at maturity) based on the interest rate prevailing in the market.

The present value of interest payments is calculated using the formula for present value of an annuity and the present value of the face value (also called the maturity value) is calculated using the formula for present value of a single sum occurring in future.

If **r** is the interest rate prevailing in the market, **c** is the coupon rate on the bond, **t** is the time periods occurring over the term of the bond and **F** is the face value of the bond, the present value of interest payments is calculated using the following formula:

Present Value of Interest Payments = c × F × | 1 − (1 + r)^{-t} |

r |

The present value of the face value (i.e. the maturity value) is calculated as follows:

Present Value of Face Value of a Bond = | F |

(1+r)^{t} |

Therefore, the price of a bond is given by the following formula:

Present Value of Interest Payments = c × F × | 1 − (1 + r)^{-t} | + | F |

r | (1 + r)^{t} |

#### Examples

**Example 1:** Bond with annual coupon payments

Company A has issued a bond having face value of $100,000 carrying annual coupon rate of 8% and maturing in 10 years. The market interest rate is 10%.

The price of the bond is calculated as the present value of all future cash flows:

Price of Bond = 8% × $100,000 × | 1 − (1 + 10%)^{-10} | + | $100,000 |

10% | (1 + 10%)^{10} |

Price of Bond = $87,711 |

**Example 2:** Bond with semiannual coupon payments

Company S has issued a bond having face value of $100,000 carrying coupon rate of 9% to be paid semiannually and maturing in 10 years. The market interest rate is 8%.

Since the interest is paid semiannually the bond interest rate per period is 4.5% (= 9% ÷ 2), the market interest rate is 4% (= 8% ÷ 2) and number of time periods are 20 (= 2 × 10). Hence, the price of the bond is calculated as the present value of all future cash flows as shown below:

Price of Bond = 4.5% × $100,000 × | 1 − (1 + 4%)^{-20} | + | $100,000 |

4% | (1 + 4%)^{20} |

Price of Bond = $106,795 |

### Bond Yields For Security Analysis And Portfolio Management Mcom Sem 3 Delhi University Notes

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