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Lesson 1 Financial Markets Instruments Bonds Institute of Economic Studies Faculty of Social Studies Charles University in Prague Welcome to the course Financial Markets Instruments. This section is devoted to bonds and in this lecture we will introduce a number of important concepts and discuss basic approaches to the valuation of bonds. We will also learn how to measure the return from an investment in this security. This is the essential groundwork needed for understanding the subsequent topics of this course. If you prefer to continue without animation, check the box, Show without animation in the Set up show settings. If you want to continue with the animated presentation, all you need to do is keep clicking on the sound buttons in the recommended order. When the button turns dark red the animation is finished.

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Essentials of bond pricing 2 123T-1T Parties of a bond contract Issuer (borrower, debtor) obtains funds from the sale of the security and pays the interest rate called the coupon rate Holder (lender, creditor) invests funds in the purchase of the security and earns coupons Properties of a straight (plain vanilla) bond

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Essentials of bond pricing 3 12...T semi-annual bond zero-coupon bond Size of coupon payments 12...T variable-coupon bond (inflation-linked bond, floating-rate bond) Redemption date 12... perpetual bond, consol 12...T callable bond Frequency of coupon payments 12...T

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Essentials of bond pricing 4 Credit risk of the bond Currency denomination of the bond Issuer of the bond government bond (Treasuries, gilts) municipal bond corporate bond (senior vs. junior, secured vs. unsecured) investment-grade bond (i.e. AAA, AA, A, BBB) speculative-grade bond (i.e. BB, B, CCC) junk (high-yielding) bond domestic bond (issued by resident in resident currency) foreign bond (issued by non-resident in resident currency) Samurai (Japan), Yankee (USA), Bulldog (UK), Matador (Spain), Kiwi (New Zealand), Alpine (Switzerland) eurobond (issued in non-resident currency)

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Essentials of bond pricing 5 Fair pricing of financial contracts Time and risk value of money A given nominal amount of money obtained at different times has different values (the longer the time until the monetary amount is obtained, the lower its present value) Time comparability is achieved by operations of discounting (against the direction of the passage of time) and augmenting (in the direction of the passage of time) Otherwise one party of the contract (issuer, seller) would be favoured over the other or would be at a disadvantage vis-a-vis the other party of the contract (holder, buyer) Present value of the stream of cash flows associated with given financial instrument must equal zero

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Essentials of bond pricing 6 Annual discounting of annual coupons Semi-annual discounting of semi-annual coupons Annual discounting of semi-annual coupons Semi-annual discounting of annual coupons

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Essentials of bond pricing 7 Valuation date differs from the issuance or the coupon payment date Day/year conventions ACT/365, 30/360, ACT/ACT

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8 Essentials of bond pricing Full (dirty) price = clean price + accrued coupon (it is the transaction price in principle equal to the fair price of a bond) Clean price is the quoted price (without the accrued coupon) Terminology Triad of coupon days

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Essentials of bond pricing 9 Summation formula c … coupon rate m … coupon frequency r … required yield Properties of price-yield relationship r P

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Essentials of bond pricing 10 Price of a bond may change simply because the bond is heading to maturity T premium bond discount bond par bond Economic jargon The price-yield relationship, which we already know, helps explain why bond prices react immediately to changes in market return. But it is not the only reason for a change in the price of a bond. This may also happen when the time to maturity of the bond is reduced due to the passage of time. We already know that bonds whose coupon equals the market yield are called par bonds and should be sold for their face value. This is true irrespective of time to maturity. The price of the par bond thus does not change with reduced time to maturity. It is easy to prove that bonds whose coupon is higher than the market yield should have a fair price higher than the face value. At maturity, however, the price must be equal to the nominal value. For this to happen, the price of the bond must decline gradually in response to the decreasing of the time to maturity. Using analogous reasoning we can conclude that the price of a bond whose coupon is lower than the market yield must increase gradually in response to the decreasing of the time to maturity. All three possible patterns of price reaction to the remaining time to maturity are shown in this picture. Notice here the new labels, “premium” and “discount” bond. The terms “premium” and “discount” come from economic jargon for describing the relationship between the price and the face value of the bond. To repeat, if the price is equal to the face value, then we say that the bond is sold at par.If the price is higher than the face value, then we say that the bond is sold at a premium. That’s why we use the term premium bond.Finally, if the price is lower than the face value, then we say that the bond is sold at a discount. That’s why we use the term discount bond.

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Essentials of bond pricing Definition of YTM Interpretation of YTM Disadvantages of YTM Ignoring reinvestment risk (in contrast with the term deposit) Implicit assumption that the bond is held to maturity Discount rate at which the present value of discounted cash flow is equal to the market price of the bond LHS … terminal value at maturity of a bond that results from investing an amount needed to buy the bond at an interest rate equal to YTM RHS … terminal value of accumulated cash flow from holding the bond under assumption that all coupons can be reinvested at a constant YTM Other names: redemption yield, internal rate of return 11

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Essentials of bond pricing 12 Holding period yield Current (flat, running) yield HPY must make assumptions about future values that are uncertain Exact YTM for perpetual bonds, approximate measure for other bonds (finite maturity, ignorance of capital gains and losses) Used for bonds that are approaching maturity in order to ensure comparability with money market instruments Simple yield to maturity Smoothing capital gains/losses over the remaining life of the bond Money market yield

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© O. D. L ECTURING L EGACY 13 Essentials of bond pricing That's all for today. Organize your knowledge carefully so that you have enough head space for more knowledge which is waiting for you in the next lesson. There will be no shortage of new information, after all, what can we expect from the rich theory and practice of financial markets? Therefore, the final relaxing sound of unobtrusive rain could come in handy. Have a nice day.

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Chapter 2 Pricing of Bonds. Time Value of Money (TVM) The price of any security equals the PV of the security’s expected cash flows. So, to price a bond.

Chapter 2 Pricing of Bonds. Time Value of Money (TVM) The price of any security equals the PV of the security’s expected cash flows. So, to price a bond.

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