In this final look at spread, we define discount factors and the zero discount factor, before bringing all three articles together to define exactly what spread is
![highjumper highjumper](https://thewire.blob.core.windows.net/web/images/default-source/default-album/highjumper.png?sfvrsn=a26fb05a_0)
In Part 2 we discussed BBSW and Swaps (click here for "What is spread? - Part 2"), and while explaining these items, the concept of a discount factor was brought up, as well as the concept of a forward rate (see the Appendix – calculating swap in last week’s article). This week’s article will extend the concept which will allow us to finally define what a spread is exactly. Again, there is a bit of maths involved, however don’t worry if you can’t follow the maths, hopefully the concepts will be clear enough for you to understand and you can leave the maths to us.
What is a discount factor?
A discount factor (DF) is a multiplier associated with a cashflow, which converts the value of that cashflow into its present value equivalent, that is it converts the future cashflow into what it is worth right now. For example, if I invest in a bill of exchange (bank bill) with exactly one year to maturity paying 2.5%, where I receive $100 face value at maturity, my discount factor would be as follows:
![](data:image/png;base64,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)
We discount by dividing by 1 plus the coupon.
Therefore, for every $100 face value invested, I would be willing to pay $97.56, or:
![](data:image/png;base64,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)
Discount factors are useful because they allow us to price a security’s cashflows independently.
Many people are familiar with the concept of a yield, or an internal rate of return, which is often used to price a fixed rate bond or express its return. The yield essentially solves the sum of a series of cashflows to be received by the investor from the bond; thus, it weights each cashflow by where it occurs in time. It reflects the time value of money that is where the value of a $2.50 coupon in year one, is worth more to the investor than a $2.50 coupon in year two.
Although the yield method provides a way to compare investments, it can make it difficult to ascertain exactly how an investment’s returns are distributed over time. An alternative method we could employ would be to value each cashflow independently using discount factors, and then add these present values to arrive at a suitable price.
This might seem a little confusing, so let me give you an example:
Suppose that we have a fixed rate bond that pays semi-annually, with a fixed coupon of 2.5%, with exactly 1 year to maturity, which trades at par. Let us also assume the same issuer has a bill of exchange, which ranks the same in the issuer’s capital structure as the bond, which matures in exactly six months (i.e. when the next bond coupon is due) and is currently being priced at a yield of 2%.
The bill of exchange is priced as follows:
DF= 1/(1+0.02/2)=0.9901 or for every $100 face value invested, one would be willing to pay $99.01 now.
On a yield basis, the bond would be priced as follows:
![](data:image/png;base64,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)
These two securities, despite being ranked the same in the capital structure, and thus theoretically displaying the same level of risk would produce two different answers as to what the discount factor should be at the first coupon date (six months from today).
According the yield method, the present value of the $1.25 coupon due in six months is $1.2345 ( $1.25 ÷ 1.01.25), however according to the bill price, the appropriate DF for that period is 0.9901, which would mean that when valued as a standalone cashflow, the $1.25 coupon should equal $1.25 × 0.9901 = $1.2376.
So which valuation method is correct? Since the two instruments rank pari-passu (rank the same in the capital structure), the bill of exchange maturity cashflow risk should be the same as the bond’s mid-year coupon risk. As an independent cashflow with a market price, the six month coupon on the bond should be valued using the discount factor derived from the bill of exchange price.
As we have market data to provide the appropriate discount factor for the first six months, we can effectively ‘hard code’ this into the calculation of the appropriate discount factor for the second six month coupon payment. So if the present value of the mid-year coupon is $1.2376 based off the bill of exchange, then the present value of the final coupon and the bond’s principal must equal $98.7624 (i.e. $100 - $1.2376). Or the discount factor attributable to the final cash flow is $98.7624 ÷ $101.25 = 0.9754.
We have just stumbled onto two important concepts: zero coupon discount factors and bootstrapping.
Discount factors, as described above, are known as ‘zero coupon discount factors’ as they are used to individually price cashflows (as opposed to discount factors generated from a yield). We look at the zero coupon discount factor, and the zero curve in more detail below.
Bootstrapping is the process whereby we use market information (current security prices) to generate discount factors (and forward rates).
Zero coupon discount factors and the zero curve
The simple example above demonstrates how we can ascertain zero coupon discount factors. Using the discount factors we can calculate zero coupon rates, from which we can then build a zero curve by calculating data points.
So how do we calculate a zero coupon rate? The relationship between discount factors and zero rates is as expressed below:
![](data:image/png;base64,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)
Using the example above, the half year zero-rate is calculated by:
![](data:image/png;base64,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)
The 1 year zero rate is calculated by:
![](data:image/png;base64,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)
Spread?
The zero-coupon swap curve is derived using the published BBSW and Swap rate data combined with the bootstrapping method above described. If we used the discount factors from this curve to price market securities, in most situations, we would find that the swap curve does not solve for the security’s current market price. Why is this so? Previously we noted that the zero coupon swap curve reflects both the rate at which the major banks are indifferent between receiving or paying a fixed or a floating rate, and that it also imbeds a risk premium for the major bank as a swap counterparty (as there is a risk it may not honour its swap agreement position in the future).
Given this, it is unlikely that any individual security will price at exactly the same risk level; hence, a margin needs to be added to each zero rate – it is this margin that is the spread we often talk about.
Let’s use the above example to calculate a spread:
- We know that we have a bond with exactly 1 year to maturity that pays 4% semi annually, and that is currently priced in the market at par ( $100)
- Let’s assume the zero coupon 6 month BBSW Swap zero rate is 2%
- Let’s assume the zero coupon 1 year BBSW Swap zero rate is 3%
The zero-coupon 6 month BBSW Swap discount factor is calculated as follows:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVAAAABhCAYAAACAufllAAAQdElEQVR4Ae2dX27buBbGv1zcbThI4q4iLjo3TtI1NEBwm4c6ewhQ96Eu6j1EL8kgmHQN48TFBHFXUTeFvRAPSJE2JVG2KMmyZH0BAtsyeXj4o3TMf+dwZzabzcA/EiABEiABZwL/cc7BDCRAAiRAApIADShvBBIgARJISYAGNCU4ZiMBEiABGlDeAyRAAiSQkgANaEpwzEYCJEACNKC8B0iABEggJQEa0JTgmI0ESIAEaEB5D5AACZBASgI0oCnBMRsJkAAJ0IDyHiABEiCBlARoQFOCYzYSIAESoAHlPUACJEACKQnQgKYEx2wkQAIkQAPKe4AESIAEUhKgAU0JjtmqQmCK+84x2v0fVVGYelaIwH8rpCtVJQE3AqM+2h8fZJ5mu+GWl6lJIAEBGtAEkJikagR+oN/uYsBQ4VVruMrpyyF85ZqMCi8nIIbsN9i7fcTw+yNuL5vLk/NbEshAgD3QDPCYtYwEGjjzrsuoGHXaQgLsgW5ho7JKJEACxRCgAS2GM0shARLYQgI0oFvYqKwSCZBAMQRoQIvhzFJIgAS2kAAN6BY2KqtEAiRQDAEa0GI4sxQSIIEtJEADuoWNyiqRAAkUQ4AGtBjOLIUESGALCdCAbmGjskoLApPfY/lhPBxhurjMdySQC4Gd2WxGj+FcUFJIWQhM7y/x/to3nDadmpc38M4YXMTGhtfcCNCAuvFiahIgARKYE+AQfo6Cb0iABEjAjUCqYCKj/jG6f8cU9KqDW+8d4gZIS/NqkTsn6A2v0NKf+UoCJFASAiLa1QW8n0qdnSY6t9dwmhEx4rTqSp1+ecRV3APvmh5pdVT5DnoYXh1q1Za/ijnQNH/PX9uzo/+1Z1+fjdyT+9mHI8t1I4l4q/N++GsS+mYy++tDe3b0dRS6zo8kQAKbJzCafRXPt/F86mc5YAdiFVXPd8huTP7qSFsSaw8SpxcFp9Tx+avUQdi0qB6xFZplG8LvNLG3axjoxjt4tx00d4BB9xL3y5Y9d5povw73UxvYPQCae+HrRhl8SwIksBECo34XA5ygZ/TOWlc9nIrn/ebbyl0O0/ue7LmKRTyzt9k466LzChh7vYDNcE0voLjrKIJvH89PLnAFm9KATjH5JYrax27Y1jXe4eIUwGyM4bPNgi7JC6B19cgVUtdWZHoSWDuBH3gaADj9IzS1dog34nn/6eFutEyJKZ6HYyCm4/S63QzZDNf0omxXHbMH305tQOX2uuY+zA6oxtd6cyLfjn9bDOh0BMERMXm1DL6SAAmUiMDoH3lEim10uLvnR/3/NbE87/MqTOFvybV0ugA0dvdlyoXNcE0vup+uOvrBt53mb+f18d+kM6Ba0XYrdrFIiv81iXbrJy8Yz4BmIK/oRq8Y8ocU50cSIIHiCEwnL7GFRY2fLWkDvp19wVI7O8/qmh7IruO88MRvUq3Ca0UPIuP3ULkHuxEDa8s7vb/BAPvohacDQuL4URGwrEquZLNid8TK/ExQDQJruje0R9fKZz6Wkr++gZ9j/J6ILmdsQvWFa3ogu46rdIp+n8qASkXDC0iGbG0kjUvqrZrXADD4eAwxpTL/e9W2TgfMv+ebBYHWFYbfrxaf+Y4ENIES3xut8w6aA08uMO8ZW5/iPMdc02sERb6mMKBqorbZRmQRXWmufwlO34T3Uql5jcA+T3/v1TAwpC8SQZFlGcftvnXYa1akikZZ7aNj4xPfloGAOGm0sn9ylw7Qee/B+/8xPFURsSp/e9mT7reBOVbX9BsA425ApxPIBXjL8NzXXxlYWw9VzZ3irbmS53fVY4cG028SuJg3XbrZdgPw4ovUPwphn+tDXA17QLuLXxXYqlXphzW+cfhNCgL+QtEYcqGoZR9/B4xfXBnCKA7fRb4d9f3YBRE74JA+Nx0j2sVfcDegehEoxgDI+UwRnuTtRcQ7QQ/tw6DF1qWoE4LyCkAHt8PH1VMm8XUs/hu10+DgwnKjyR8g2x5YBzXXNM/loAGTlpXAmu4Nf6HIHqBFP9cR45eYkdrauHOCN1FDYJFiT79eHS1qAHA2oKOnBynJDusH7jyx1yu42VYXredOoxvodQr9qoyng0vVfB5FLZbAiMjj91yVTOGCFphC0GXKXbiBDbVmj3fughorX8gxygAw1vO8xnB9+jzEGPu4aBhpXRd4SjzPZdDk200QWNe9sbsvHWRkWMCzoKu2fq4DTjUudR/dqQ3255aOlEVQXPp16mhRQ1xy3MZkt/y+bGEQunKv2GnP5seuhva2zfdh5QSgcROd8/Acajih/1kYt8/oYvjlBBi/4Pn+0v/8/UZ6OAye+ui3e8CnRz/N7AFPoU2/Qka7+4LOn48QQ1chS3tTie+e3qi8Vvk/lGJiX9kjem8BCKMo5Ih/w3ND3mynwJOpz8pNyPZ682oaAuI+PYaY35X/qbbPucmQ95YuT712lrrppanXmvM0WhB73TEeIugfY1sTWfDph56zqJY/0O8+yOflU6INmUvSO+kY1STNFTcDGrcJXgwbji58o/dnTFAAPf+ZQEvZy222gTvjRj86RtxNp72X5FBi9oAhukFvpgHwZmgEPAjPz476MjjKac9II37N4G+5EPKF61ms/ECd1I+MdY5YfbdKn4A8fsiPgFjEu4AnRjbqx613OpYLGqsfdK2Fgwz5XByjOzhBT/+Yfvd/YMfXF2j39Q+vll3m1wbOLk6kt5D3eeG26btONtH5FOyVJqqJ5NPF4LSH4ZIARHNZK9Nn01EvfrsE304+hBfKf/SH78Jt6/2RXkPzq2cOd+cV1m/MvLMHdNsvSyK4KCPz08PvC9F784WIX/Gu8JV9bRg5LV+9SgCvOlj8kvmr/s3OYmjgz9cEvSGkwX7VwfmK+ZeIfPWD0mwbc53q2umFpfesvzN66DZ9QtXix5wIxPpJD7rSl/u8tdoIOMuQ0YqCIzLpPy7KHPyD0dVhsmFrTgwyiRHTA3/uy0Xd+fMfNx22pCD5LItobiLvd9v6RzCzU3pHHedTf2aRhn1bGXw7Ps7Ipr6JicikIj3FR32x5JN5OrNF0CdLGkv0FlFzGSHmaEVeEcElkEaGmope0ygj6W366MRlf1W6H32dmQG5yqt1NEqP1jV5RKE8ZIhSNTvj/lL3t0skIK0/XzdHwG0Ib1rpdb8Pu4Gq1f/YYnXvzth7qhdsFg5Tqkdq2UEQ3BmgNvybe10t8v0FtWBvdlmPMvpdvD6x9SzFF2KOSw2FqxK3VbsfW9o+mS93Gl/ruMZS+6HN9QC5XaeHA69qQ/u4OtbjegkNqJrHCCysTHF/8yC7/LHbHISBRTC8nhxym0FL1B5WuYNATCvIOSg/mow57zHqq/lcc17HIl/eIlK+MCh9iPlyPY8ivxN7WNv+dbFCL6PRmNFsrPqU/cZTxlNsLzMWx0qvdWZf7hx9rfV6gHkvSICHuBLhIAfd2Pn+snOum37J50CLJCPmMb4Abb0NSJQtVrWH8XNU0d6dvzrY7BgBT+QqnQdPyDW2Fsk5qXZ3Ma9rKSsqH5A9l789vG8P5ZyunEJV7mrdI39l8XZ4pfawqt6mOV8ao0+RqF3LkjEaxQ6J2/i2cJVZRHr9w2bffpdMgzxkyK1uojMg7jHbD5DoifZe0P54gf5uzIJsMnWZqggCm5s9YMmVI1Dhebql85w6GrkRad3WNrnJWDlvrOZIP9zPwmc22PTitc0RKOEQvoifDZaRhsDozpPTJKsdIdJI3/48YsW3OxC99+CqfLTmi2msz1XbLxqtzFZfoQHd6ubNsXLTb7iREcmjLro5lrI2UUkWioILiVFVssiQ22U8LNm+Fyqvde4fczEcRWPqhpLy4+YI0IBujn2lSpY7GkRAF2OXQ5UqoIP+2nT257eBVfOjqWWM+jLSUMBRw6ZI4FoD8piLwGJqIAE/lIAADWgJGqH8KujzaZIGeyhhjUw/6ZB6cnEo7J0WSiM/ppLhux6GD1KziQ9f0wZ78FQlj6VwLbb7Mw3odrdvPrVTe2ArfY6Vk590jC+3kwwfvfRcaprecbpJ/DKWupC2/pAnXiK8J1qL4OvGCdCAbrwJKqCADmHoHPRaGaJS+Hxn85P2W8lRhoqx4Ls+B+M66NgRyyMYqXOBIgE8KnDP1ETFcu4DrQn8qlQz6RxhoD5G/INArIBAooI/OPpJW7VzkKFDP1rlJLrofi5QIrFMlBsBGtDcUG6voMRzhBKBcWxJjkj8Vex99LK6jsZEOA+q6oclPAteXHxKJAMQUbx0MJxFZrd3/sr/8kjwbhKZOk8CHMLnSXMrZanoWInqJobsN9i79eOg3l7654UnyspEVgJ6IWlxXro1GS9uiAB7oBsCX51iLYEvYpUXPbfr2G/5RQYCciHpsFpH22SoblWysgdalZainvUkoLZO1bPy5a81DWj522izGupTWDerBUsngVISoAEtZbNQKRIggSoQ4BxoFVqpTjoa25+i1R5DhgkMfyFCwy05U0ccHlf2P3FGE/+qR4AGtHptVqzGjV0ciMMYiypV7LP8rg7CMsrMso2JxskAybe5EuAQPlecFEYCJFAnAuyB1qm1U9VVuxO+YDIFWsYBpKnEVTTT/GRIQ/+VJzYaaVO/1WeBWY/JTi2VGXMiQAOaE0iK2VICek5WHsG7CIQsDao42/13D0Pb0Rw54dButKtileZUHMU4EuAQ3hFY/ZIrf+zZGL8nbrXXZwiZB/a5SShJ6riz3XcAiLPdS6Im1SieAHugxTOvXIku/thysec6tOT005sf2FfIsDdPwmJRa2gTWMzUho5DwGNUbG2w+Ws0oJtvg9Jr0HjdRtMbw/fHXj4J2ji7xjA2Ckf6qq5LbnqNXFxc05ai4xDsY3c59rQFMF9GAhzCZwRYi+xqKxOHq0Zrx57tbqTJ+lYHso6cH59VMPPnRYAGNC+SWy3nEG9ORQX9lfitrmqiyk1xv+xs90QyVieq+jlUq2tY/RQ0oNVvw0Jq0DrvoIkxhs/TQsorcyGj/gW88Ql6S7yfsuu/BedQZYdQegk0oKVvopIoqM4DGnt3tV51Fotkyc52z9huHL5nBFhMdhrQYjhvQSn6PKAHPNV0347vTupwtnuGVh/deRijic75YQYpzLpuAjSg6ya8TfJb5+i8AgY331C7gXyqs91TNv70G24GQLPTxRlX31NCLCYbDWgxnLeklAbOPnXQHHv4fF8nE5r+bHf3hp/i/rOHsfUoZHdpzLFeAjSg6+W7fdLFgWq9E4yvL7D0TPMtqnmms90dOUzve/DGTXQ+vePxHY7sNpF8ZzabzTZRMMusOAHlI3765RFXrYrXZZn62hc+Lo1087zOZagt/esHJ9lPHo3TlddzJ8AeaO5IayJQxu28wd7Tds+HZj/bPeH9IOY90cMw67HNCYtjsnwIsAeaD0dKIQESqCEB9kBr2OisMgmQQD4EaEDz4UgpJEACNSRAA1rDRmeVSYAE8iFAA5oPR0ohARKoIQEa0Bo2OqtMAiSQDwEa0Hw4UgoJkEANCdCA1rDRWWUSIIF8CNCA5sORUkiABGpIgAa0ho3OKpMACeRDgAY0H46UQgIkUEMCNKA1bHRWmQRIIB8CNKD5cKQUEiCBGhKgAa1ho7PKJEAC+RD4F3EWbEmY4AGbAAAAAElFTkSuQmCC)
The zero coupon 1 year BBSW Swap discount factor is calculated as follows:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUQAAABbCAYAAAALHfw8AAAQiklEQVR4Ae2dW27byBKGfx+cbchwzKwiCpJjxcoaYiCY6GHoPRgY5SEaRHswX+xBMM4aRraCMaysIowDayE66Ga31CSbN5GUKOoPEIgim9XVH6lyX6qqDxaLxQL8RwIkQAIkgP+QAQmQAAmQQECABpFvAgmQAAkoAjSIfBVIgARIQBGgQeSrQAIkQAKKAA0iXwUSIAESUARoEPkqkAAJkIAiQIPIV4EESIAEFAEaRL4KJEACJKAI0CDyVdgBAnPcuG/QG3/fAV2p4i4T+O8uK0/d94DAbIzeH7eyoU6vswcNZhO3SYAGcZv0WXcKge8Y94aYMLA0hREvVU2AQ+aqiVJeBQTEEPkKR9d3mH67w/W5U4FMiiCBbALsIWYzYomNE+jgzLvceK2skATYQ+Q7QAIkQAKKAA0iXwUSIAESUARoEPkqkAAJkIAiQIPIV4EESIAEFAEaRL4KJEACJKAI0CDyVSABEiABRYAGka8CCZAACSgCNIh8FUiABEhAEaBB5KvQeAJPv3ypoz+dYd54bangLhM44Daku/z42qv7/OYcHy4DQ2hrpXN+Be+MyR5sbHhufQI0iOuz450kQAItI8Ahc8seKJtDAiSwPoHU5A6z8RsM/0kQ/tzFtfcOSYOW1Hu1yINTjKYX6Orv/CQBEtgSAZFhaADvh6r+wIF7fYlCsxJG7krdiP6fd7iI/sDnX+F+8OCnpXaz2oacOq4tH0jtIXYv7jB6GzRNNEykYpL//3Lh+B4+nLzBeKabHv407xXzPct7pYwruM8B9F/TGIax8RsJbIGAyD05gHc8Wv5OR30f3m/Jv++wkiqj+R+3MO2ESNs2+eMN3Js1lsJitqGsjmGNk2xPqkFcijhwcHS4/AZ03sG7duEcAJPhOVLbe+Cg9zLaj+zg8BhwjqLnjTp4SAIksBECs/EQE5xidPFiWV/3YoS++H1ffc1c2Z/fjGTPUnR8zN5g52woOz6+NwrbiKdH+KI+3cEyP0Vn6wDov1rpIpQqpOMa8nXDMwziHE8/RdFnOIzars47DPoAFj6mD7a/ACn3AhA9SK4S6sfATxLYFoHvuJ/YRmsv8Er8vn94+JIwCgw0nuNh6gMJHZ+XPcduI2I9wEDa7IsH33HxPjTMXkPHQvJX7DMNonQBc57B7CDq27uvTuWh/8tiEOczCE5IuFfL4CcJkMAWCcz+lds02EZrh0dBpvKfT5bf91LlOQI3UUunCUDn8JksGbIR3QtMjd7oUhQCw9cfRNYmiupYVP5KgfQ5RGhFet3ExRMp6+dTvFstuq0LwAndK+YBMobYhnI8JAESqJfA/OkxsQKrMYuV7iCwm49ItZux++In5jdXcuj+KtQ7BMrrGNSVJN/UJHWVWStyHBsvmyIAHB/GDKbt3kChZxhFh98Rca37all9y2xjxip+5v0s0B4CNb4/Ogoo8zeeSDNYD8APH7+eRJcwsWDGhe/44vlw3GFsobW8jqLqZPmmYqkGUSoSXVAx7tZGzzilDtW8AiBXmcQUxfLf8551+L283sYD0YX/dtHGlrFNmyDQ8Pen+96FM/HkAuuR4aqTFW1kogs6Sw7c2AKsWWr947zyUwyimsh0ekjSUVvu6IoQoOYVQr5EgQ/RNDSEXr+BvDNOoHfyJn6SZ3aCgHBL29l/0usE0rdQuOp4qiFi1fn6fCRDMG1zlKv2Br039EfF/B5XAjKO8stPNojzJ8gFZstwOKhdGUxbD1LNPeKt6WcYdK1tXXPpxI1RwkRrRlt5eUlgp39Uy1bwYJMEgoUTH3LhpGsf76YbM6WtMIrTdzHVZ+MgHt32u9eFl72392FXG329rI5Z8nU94jPZIOpFkQRfQVmJ8DR/O4hZdT2UjoIUrjbmfGmoS60cwE3lWnNc4xxQaxixIckEanx/goUTexIN/TtOM2bJSosryvXu4BTRhZLVfar35riJI9FyOmbLX+mSYhBn97eynB2GqkQMiS3L53ruMe6QbVQ9G+MThph+QxAyZFxKPdQvRyi0yAjpeRvpaUbCeGxZUkKGWVduyFmGIaqFDuhMLCEd9I2Wz4bPAVk05qkmEajz/Tl8Jh2hZWq1s7C7i/4dh4IyinCZfVEO2+9DHSFThO5YxVxtzEIldMwl36grwQ8xzbIL4zOUvkv9kS0OWQ2lbc7cRsXoXhR3zBbG7f41pt9G6MOH9+W7kig2Ng886835TGHoer95OB4FIYcilCiaU08Yuw8e4P6lwhL/DHwrtRxx/f7VHabivP+Ih5vzwJALj/qU+VWzqTwmAfEeiTne5f+xfne3zKbThfCdhj9FOL7CtoagQvRSQnZXrfmO8fAWeO7iY2JAtFp8fR51xF5JkUeFdDTvzSnfuMVuEJOcqkXv7GQAz3ekATHDdJYy9fzh8kSFB2KeQvZIlRe96f8o5jxND/f5V3zyfBlbadVTqDUby+QV/VEkiN2YFxXDfHG/HD4sbjHFMDDkQpeU5BYVtpqidpyAHGFMgt+MjOkXf1z/Ga4X41s5iw7OBqcymsT7tArTC0LlHLgfw73GXNVLOzHEpD/CNO03onuQmQuta+qYW/6qVfE5RD0kFWV+iAQOes0ouMmavULLM+9d3GLYeyyeMUPLyviUE62TR2jXJxHyczy4W7pByRAgnGKgJi31sNg5H67KiGmByF+nYN4k7nUvhw+pf+0yFOblvSYg/OuWHaXua/QPbjGREV72hYyNwhJD8r+eyVXi5e895CGSTxtp+EV2LHHvt/B6QVzCHDdXt7LsYAkmXmp5prCOBeXrikTG7O3+e1r8/XtvcfJ5VkyNh8+LkxN38ffTYrF4uln8/vvNQhwG/2aLzye9xcn/jP8nnxcP+rL8VGVC9SbpEpz/XVYWEsIvJLAGgeDd4/u0Brqab4n3ELWlbPqnmGjFLX49ib8EU/Q+Xi57flp12wKKvqY/Qyvhyy525K+2mkI4HkTOayH8JIECBORw1HFxnadnVEAui5Yn0ACDqIPDRTz0i5hRS2xi5xDHMhJmAGn4QrYqiK8MDUnEcH5oDuEjZeSCDWTKI5naR5QXCzhizlKmE3LQs2W4SFSQF8oTMLwHhLC8q/qhiovJWA77DBl5/rAaxVMPxdTNcCISI68xN5cqmRcrIVBzDzRZvBjmRoe1YogbG9omiVDD29BQ2SgblR8aGqtyYtith9VSjpIpzhnln/52C+hl6MDDEgTiUxoPn4MpkM/huY+UOgrI0O9C5P3TdZrvQ0qFqZekrIj81Bt4ceMEsPEaq6pQGrzovGBVwiln2wTsxkMZuKQ/ghGlC8kw56RDclSdJQ0Z/6iGoDb2i93tppK+Z/VCxHBDblkgna0fMeB+LAUgKx+y3hip+T4LSKyvqPKBiyX5zJu0VGhWUIZYxZxG3K9kAy3prcT71yuQGn82Dnxdrw2/XSHDXbm51MeSkosQaMAcYn51hevL5PINJiJiZHqRf74xfxUtLanm0cSeGZ49XrRRDdd5OC1ho3niWmVbqpAhBak5btMJX8btHsp9SHq/IpFRMZDK/WMBuUdJyInt7YjvcIzXdk/slEEUTtJTZtEq+MYoYwgX15Ywy4LCNlJcx9DaKtNxrUEG5tBKWqh4FTKEwOTQrxe4uHbx88MQ7tFVStSViKK6w1lIO35pKoGdGjI3FWKT9ZIbAInIonUiDrbUMOkEL/MOJxu8LNXKyxDZ3VdhndZoJ9FTHJ3Cvxwk7j6ZpSevN4sADWKznke12qjwxVCURLU1tE+acLeSMcdBvH5mA7vv5c5yeXany5TFAlsnQIO49UdQnwJB+KJtG9j66tx5yTKzjN6DXCUR+S1tAUXF2f7w8Cl1P96dJ7MXDaBBbOtjnn/FldxeMp6vsulNDhZOECQtTVA2FGFkKVOFDOAFLqZBFqXY3sJmnaqXGM2kZBbh8W4QoEHcjedUWMv5w1TueqjTmBUWsMUb9G5vNhX0Yok9T+fqjipkBNKUq89CbaK0qsI46kDuP5y5h7FxCw8bSYAGsZGPpaxSevPwtEzFZeuo8X4zIWikGrlYYqRni1xefa1Cxkpa5pE2wJP7huQ5zNSYBWwEaBBtVHb9XFI+y11pV6GEoMrhPJq0tJAM4V5zjp7VaT0tWbIBVKb0ghjnx/coN4rxsNkEaBCb/XzW007vh5OZeDMqXhmXrWdzXjMhaKg5a8gQOTwj0SOz8SBIg+8mp8EPqlURLbHM0yGl+KXhBHbKMbvhLBujXt55tpDCRnJfp7e+/19IZpkvhROCWiorIKNzdolrnOPDZSQpskx2aoTcWaoJTlW1YXtiBbywAQI0iBuAvOkqcs+zScWEA3JOn7sCDZEZyr1nGJWJN5chcvGtLcNqZESC5JIRSBRGcVoipCR3WGG4AfzWIAIcMjfoYVSjiprzyiVMDJGvcHS92oQr120sZCWgF1aCsEJrEZ5sOAH2EBv+gIqrpxPuxveFicsSvavL+GmeKUdALqwUSHZcrjbeXSEB9hArhElRe05AufrsOYWdbj4N4k4/PovyYjtWy2meIgESyCZAg5jNiCVIgAT2hADnEPfkQdfWTMNdJ16Hj+HJbfy0SPCbsIG5yDTT9H9is3n+aycBGsS2PVe1G6G/qXbJ7DDxrL3rut3Q2GzqwbEeGwEOmW1UeI4ESGAvCbCH2LrHrkPIHvE0B7oNCDrZNOK691ZObI8KmcTxIfdKSYTU7As0iM1+PtSuCAE9nxkJt5MG8nKA7A2hilQWL6tDJrNyNcbv5JmmEOCQuSlPojI9VExtav4+e2V6H5KdTnR64MA1t/sE0L0Ikrxi8u8ObMFqfzY8uxkC7CFuhvNGaykSUysXPy4jSzA/VgkOnPO0HeU22qzsysQCz9RWbDPTCDqGvPdyD+cpbNh38BwN4g4+tCyVOy97cDwfWVt1CjllExok6VKX3KT60s8XCWdMl5R8VceQ5wmZTJbCK9slwCHzdvnXU7tyveEQUeFVm9aj/xrdeogDOilvnXXUpTvlLgnQIC5RtOlA7QOCYKW5TS0r3pY5bq5uAeEMfvGi+O0579jlPWxyNnEvitEgtvQxd9+7cOBj+jBvaQvzNUtmvPZPMUqIjMknJavUju9hk9W8PbpOg9jWh632FPG9L3u7sioWjIaT+Kpz5Y+cw+XKkW5LIA3itsjXXq/eU+QW97PaK2tcBUHoIOBeX+Ks5kXf2RcPPhy47+sbkjcOcEsVokFs6YOVzVIbqE+uvu7XTnCzMT5c+uiP6jeGmH/F1QRw3GHthrfNr2pT2kaD2JQnUYseHZx9dOH4Hj7d7Mtc4neMh7cQ/pMXtS0p64c1x80nD77j4mPd3VBdJT9rJUCDWCveBggXmyyNTuFfDjDeg6HzbDzExGqggi1Wq2QwvxnB8x24H98xdrkBr3oVKhwsFotFFYIoo+EEVJxv/8+7DfSctsRCxzInVS/D+qoZRsv46MlpuV0Fk/Tk+a0RYA9xa+g3XLHMW3iFo/v2zifO7i3JaOvALOYNMcK0zBardehFmaUJsIdYGiEFkAAJtIUAe4hteZJsBwmQQGkCNIilEVIACZBAWwjQILblSbIdJEACpQnQIJZGSAEkQAJtIUCD2JYnyXaQAAmUJkCDWBohBZAACbSFAA1iW54k20ECJFCaAA1iaYQUQAIk0BYC/weC9srL+SgC2QAAAABJRU5ErkJggg==)
If we price the bond using the BBSW-Swap zero discount factors we should pay the following:
CF(1)×DF(1)+CF(2)×DF(2)=$2×0.9901+$102×0.9707=$1.98+$99.01=$100.99
So why is the market paying a lower amount of $100 for this security? Well, compared to the BBSW-Swap curve, the security is perceived to be riskier; hence, there is a margin being added to the zero rates. We need a numeric solver to calculate this margin, but as it turns out the margin that solves for price given the BBSW-Swap zero rates supplied is 1.0099%. Alternatively stated, the market demands an extra 1.0099% over BBSW-Swap for the perceived risk of the issuer.
Let’s confirm the margin.
The zero coupon 6 month discount factor is calculated as follows:
![](data:image/png;base64,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)
The zero coupon 1 year discount factor is calculated as follows:
![](data:image/png;base64,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)
If we price the bond using the BBSW-Swap zero rates with the margin applied we should pay the following:
CF(1)×DF(1)+CF(2)×DF(2)=$2×0.9851+$102×0.9611=$1.97+$98.03=$100.00
Conclusion
So this second calculation proves the 1.0099% spread demanded by the market to reflect the risk of this issuer. Often we would quote this issuer to clients as returning BBSW + 101bps (where one basis point – bps – is equal to 0.01%). As we noted above, the spread reflects the risk of the issuer. The higher the risk the issuer represents, the higher the spread the market will demand, and the higher the return to the investor will be. This is the basic risk and reward axiom.
This concludes our look at “What is spread?” While there is a lot of maths involved (but don’t be afraid of the formulas in this paper, as noted, you can leave the maths to us), hopefully you now have a greater understanding of this central tenant of fixed income.
If you understand the basic concept of a spread, you are able to analyse and compare fixed and floating rate investments.