Let me remind readers following along that this is all based on an identity – i.e. yield = dividend divided by price.

This is not a theory or conjecture, but you were right James to identify that multiple things are going on here.

We need to test one thing at a time with this identity – the impact of changes in rates on price or changes in yield on price.

I use this identity primarily to understand relative cheapness at current rates, much the way you use your implied volatility calculator.

Readers may ask why I might assume that my assumptions about changing spread are not also changed by changing rates. I will say that I never contemplated using my model this way.

I use my model to ask simple and relatively near term questions such as what happens if the seniority spread narrows or if credit quality improves?

Using this approach I more or less simply noticed the impact that changing rates have on the resulting target prices. James’ asks a good question as to how to explain price movements due to rates. I think this has some explanatory power.

]]>*Take TA.PR.D with an issue spread of 203 basis points for example. The cash yield at reset with the GOC5 at 0.905% today and a closing price of $10.10 is 7.3%. If I think that the market spread ought to move to say 4.5% in the future, then that is the same as predicting a target price of $13.58.*

So at time=0, you’re saying that R(0) is 0.905%, the expected future dividend is D(0) = (0.905%+2.03%)*25 = 2.935% * 25 = $0.73375 and the fair value, P(0) is 13.58. This means that the Target Yield, Y(0) = D(0) / P(0) = 0.73375 / 13.58 = 5.403% and the spread to five-year Canadas is Y(0) – R(0) = 5.403% – 0.905% = 4.498%, rounded to 4.50%.

Then there’s an interest rate shock:

*If the GOC5 falls by 0.5% (i.e. to 0.405%), then my target price falls to $12.41.*

So R(1) = 0.405%, D(1) = 0.60875, and you claim that P(1) = 12.41.

Is all the above correct?

If so, then your expected future yield, Y(1) is:

Y(1) = D(1) / P(1) = 0.60875 / 12.41 = 4.905%

and the spread to Canadas is:

Y(1) – R(1) = 4.905% – 0.405% = 4.500%

So the spread to five-year Canadas for this issue is unchanged between time=0 and time=1 and the 50bp change in R has resulted in a price change from 13.50 to 12.41, or -8.62%.

Is all this correct?

]]>Y will be the future spread I choose + R(0) – 0.5%

]]>I mean X + R(0) – 0.5%

]]>With the future spread chosen (e.g. I expect the spread to narrow by X%), Y will move down by X + 0.5%. The Dividend at reset will also be adjusted down from (R(0)+ issue spread) X 25 to (R(1) + issue spread) X 25.

It is the target price that is important here though. The target price will move down.

Take TA.PR.D with an issue spread of 203 basis points for example. The cash yield at reset with the GOC5 at 0.905% today and a closing price of $10.10 is 7.3%. If I think that the market spread ought to move to say 4.5% in the future, then that is the same as predicting a target price of $13.58. If the GOC5 falls by 0.5% (i.e. to 0.405%), then my target price falls to $12.41. Therefore, to meet my required return I need to lower my bid.

]]>*If we believe that efforts at TA underway now might reduce that spread to say 4.5% by a certain date, then we can generate a target price.*

… and the other based on the general level of interest rates:

*This price will go up or down with prevailing rates*

I have no problems with the credit quality argument. It’s clear that an investor will be willing to pay more money for a security the more likely it is to keep its promises.

But I don’t understand what you’re saying about the effect of the general level of interest rates.

Let the general level of interest rates at the initial time be R(0) and let it change to R(1) at time = 1. Similarly, let the Target Yield at time 0 be Y(0) and let it be Y(1) at time 1.

Just to keep things simple, assume that the yield curve is perfectly flat at all times and that there is no change in credit quality.

If the general level of interest rates declines, so that R(0) – R(1) = 0.50%, what do you believe should happen to Y?

]]>*Target Price = Dividend at Time of Target Price / Yield at Time of Target Price*

For this to serve as an explanation of the correlation between GOC-5 yields and FixedReset prices, then “Yield at time of Target Price” must be relatively invariant, and I don’t see why this should be.

How does the model assume that “Yield at time of Target Price” is calculated?

]]>For Fixed Resets, the following applies:

Target Price = Dividend at Time of Target Price / Yield at Time of Target Price

So, for example, if we have a view of improving credit quality for an issuer and a view of when that might be recognized in the market (as a lower spread), both the dividend and yield at that time can be predicted. The dividend will be the issue spread plus the prevailing GOC rate X $25 and the yield will be our estimate of the spread likely to be demanding in the market plus the prevailing GOC5.

Everything we need to know to adjust our target price is included above, if our models relate the future prevailing rate to current rates, or even more simply – just use it.

Therefore, falling current rates result in a lower target price. Current bids then must fall to facilitate the same required return.

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