1.2 Asset Classes - Debt Instruments Flashcards
Why do convertible bonds trade at a premium?
Because there is this potential advantage to the value of a convertible bond if the share price rises, and the downside protection of the redemption value if the shares do not perform well, convertible bonds generally trade at a premium to their share value. The calculation of the premium is shown by the following example.
Convertible bonds enable the holder to exploit the growth potential in the equity, while retaining the safety net of the bond. It is for this reason that convertible bonds trade at a premium to the value of the shares they can convert into. If there were no premium, there would be an arbitrage opportunity for investors to buy the shares more cheaply via the convertible than in the equity market.
Convertible Bonds
Some corporates issue bonds with conversion rights, known as convertible bonds. Convertible bonds give the holder of the bond the right, but not the obligation, to convert the bond into a predetermined number of ordinary shares of the issuer. Given this choice, the holder will choose to convert into shares if, at maturity, the value of the shares they can convert into exceeds the redemption value of the bond.
Conversion Ratio
Conversion ratio =
Nominal value / Conversion price of shares
Usually, convertible bonds are issued where the price of each share is set at the outset, and that price will be adjusted to take into account any subsequent bonus or rights issues. Given the share price, it is simple to calculate the conversion ratio – the number of shares that each £100 of nominal value of the bonds can convert into.
Limitations of Flat Yield
There are three key drawbacks for using flat yield as a robust measure in assessing bond returns:
• Since it only measures the coupon flows and ignores the redemption flows, when applicable, it is giving an incomplete perspective on the actual returns from the bond. A bond that has been purchased at a price away from redemption will be significantly undervalued when the par value is excluded from the calculation.
• The calculation completely ignores the timing of any cash flows and, because there is no discounted cash flow analysis, the time value of money (see Section 2.6) is completely overlooked.
• With floating rate notes (see Section 4.2), the return in any one period will vary with interest rates. If the coupon is not a constant, using a flat-yield basis for measuring returns becomes an arbitrary matter of selecting which coupon amount among many possible values to use for the calculation.
Accrued Interest
Listed bond prices are flat prices, which do not include accrued interest. The flat price is alternatively referred to as the clean price. Most bonds pay interest semi-annually. For settlement dates when interest is paid, the bond price is equal to the flat price. Between payment dates, however, the price of the bond will be the flat price plus the accrued interest.
Accrued interest is the interest that has been earned, but not paid, and is calculated by the following formula:
Accrued interest = Coupon payment x Number of days since last payment Number of days between payments
Day Count Conventions
Common day count conventions that affect the accrued interest calculation are:
• ACT/360 (days per month, days per year) – each month is treated normally and the year is assumed to be 360 days, eg, in a period from 1 February 2011 to 1 April 2011 T is considered to be 59 days divided by 360.
• 30/360 – each month is treated as having 30 days, so a period from 1 February 2011 to 1 April 2011 is considered to be 60 days. The year is considered to have 360 days. This convention is frequently chosen for ease of calculation: the payments tend to be regular and at predictable amounts.
• ACT/365 – each month is treated normally, and the year is assumed to have 365 days, regardless of leap year status, eg, a period from 1 February 2011 to 1 April 2011 is considered to be 59 days. This convention results in periods having slightly different lengths.
• ACT/ACT – (1) – each month is treated normally, and the year has the usual number of days, eg, a period from 1 February 2011 to 1 April 2011 is considered to be 59 days. In this convention leap years do affect the final result.
• ACT/ACT – (2) – each month is treated normally, and the year is the number of days in the current coupon period multiplied by the number of coupons in a year, eg, if the coupon is payable 1 February and August then on 1 April 2011 the number of days in the year is 362, ie, 181 (the number of days between 1 February and 1 August 2011) x 2 (semi-annual).
Spreads
Commentators often refer to spreads in the bond markets. A spread is simply the difference between the yield available on one instrument and the yield available elsewhere. It is usually expressed in basis points, with each basis point representing 1/100 of 1%.
Spreads are commonly expressed as spreads over government bonds. For example, if a ten-year corporate bond is yielding 6% and the equivalent ten-year gilt is yielding 4.2%, the spread over the government bond is 6% – 4.2% = 1.8% or 180 basis points. This spread will vary, mainly as a result of the relative risk of the corporate bond compared to the gilt, so for a more risky corporate issuer the spread will be greater.
Spreads are also calculated against other benchmarks, such as the published interest rates represented by LIBOR (the London inter-bank offered rate). Because the government is less likely to default on its borrowings than the major banks (which provide the LIBOR rates), the spread of instruments versus LIBOR will generally be less than the spread against government bonds. If the equivalent LIBOR rate was 4.5%, the spread over LIBOR would be 6% – 4.5% = 1.5% or 150 basis points, compared to the 180 basis point spread over government bonds.
Pricing off Benchmarks
The use of a particular pricing benchmark is generally determined by the type of debt asset class. Also, specific features of a bond can mean that pricing off a benchmark security/rate becomes more difficult eg, a ten-year corporate bond, with a put/call feature, is unlikely to price off the ten-year gilt but rather a benchmark curve, as the estimate of the maturity of the corporate bond is unlikely to coincide with the specific maturity of the given gilt because of the put/call feature. (The term pricing off simply means the price/value of one thing – here a bond – being determined from the price/value of something else – here another bond.)
The comparison tends to be against one of three yields:
- Government bond yields – benchmarks for corporate bonds are generally selected according to market convention; typically, the most recently issued government bond closest to the maturity of the corporate bond is selected as a benchmark. Gilts, bunds and US treasuries are the reference securities in the UK, Europe and US, respectively.
- LIBOR (the London Inter-Bank Offered Rate) – the rate at which funds in a particular currency and for a particular maturity are available to one bank from other banks. LIBORs are gathered and published on a daily basis. At times of financial stress, such as during the banking crisis in the autumn of 2008, the spread between LIBOR and the applicable base rates can widen dramatically, which, in that instance, reflected the incapacity or unwillingness of banks to engage in normal money market activities.
- Swap rates – there is a very active market in exchanging floating rates for fixed rates in the so-called swaps market. The rates available on swaps are also used as benchmarks against which to judge yields.
The Present Value of a Bond
Money has a time value. That is, money deposited today will attract a rate of interest over the term it is invested. £100 invested today at an annual rate of interest of 5% becomes £105 in one year’s time. The addition of this interest to the original sum invested acts as compensation to the depositor for forgoing £100 of consumption for one year.
The time value of money can also be illustrated by expressing the value of a sum receivable in the future in terms of its value today, again by taking account of the prevailing rate of interest. This is known as the sum’s present value. So, £100 receivable in one year’s time, given an interest rate of 5%, will be worth £100/1.05 = £95.24 today, in present value terms. This process of establishing present values is known as discounting, the interest rate in the calculation acting as the discount rate.
In other words, the value today, or the present value, of a lump sum due to be received on a specified future date can be established by discounting this amount by the prevailing rate of interest.
To arrive at the present value of a single sum, receivable after n years, when the prevailing rate of interest is r, simply multiply the lump sum by the following:
1/(1 + r)n
Inflation and the Yield Curve
Nominal yields are drawn from conventional debt instruments and include investors’ anticipation of inflation. However, in addition to nominal yield curves, real yield curves can be observed from the yields on instruments that already include an uplift for inflation within their returns, such as the UK’s index- linked gilts and the US Treasury Inflation Protected Securities (TIPS). More detail is provided on these instruments in Section 3.3 of this chapter. The difference between nominal yields and real yields reveals the term structure of inflation – the expectations for inflation in the future that is currently captured within bond prices.
Generally, if inflation is expected to increase, then the yields demanded by investors need to reward them for the anticipated inflation – so yields and the yield curve would be expected to rise. However, when the Bank of England (BoE) or another central bank, such as the US Federal Reserve, is concerned about inflationary pressures and increases short-term interest rates to counter the danger, the impact on medium- and long-dated bonds can be that the yields fall. This is because the investors have confidence that, in the medium term, inflationary pressures will be removed by the pre-emptive actions of the central bank.
The Inverted Yield Curve
Clearly, in an inverted yield curve scenario, yields available on short-term gilts exceed those available on long-term gilts. This occurs when there is an expectation of a significant reduction in interest rates at some stage in the future. The consequence of this is that, when investing in longer-term gilts that will be outstanding when the interest rates fall, the investor is willing to accept a lower yield. For shorter-term gilts that will not be outstanding when the interest rate falls, the investor is demanding a higher yield.
The existence of an inverted yield curve does not remove any liquidity preference, but the impact of the anticipated interest rate fall outweighs the effect of the liquidity preference.
