0:17

We use actually the same formula or

Â indeed it's very similar to the one we saw for equities.

Â The net present value, as you can see from this chart here which we have

Â already seen, the net present value is the discounted value today

Â of this future extreme of incomes which you generate with your bond,

Â and the principal which you get back at the end.

Â So here to we have a very simple way of knowing that when interest

Â rates increase, this YTM the denominator, the famous year to

Â maturity when it increases the value of your bond today falls.

Â Okay?

Â So, when on the chart, we see that when Y0 goes to Y1 it increases.

Â P0, the price of the bond goes from P0 to P1, i.e., is lower.

Â And this, we can see with the following chart here which depicts the relationship,

Â we saw with the example of U.S. bond here, to change a little bit.

Â I've taken the UK bond market, and in red it's the index of the UK Government Bond.

Â 1:28

And in blue, it's the three month, short term interest rates, which we call LIBOR.

Â LIBOR meaning London Interbank Overnight Rate.

Â And it's depicted on an inverted, again [LAUGH] sorry for

Â that, an inverted rating scale, in blue.

Â Why do I do this inversion?

Â Because, well, by now you know,

Â I want to just illustrate the fact that the two lines are perfectly correlated.

Â When the blue line increases, it's actually a fall in interest rates.

Â You see for instance, between '90 and

Â the 94 the short term interest rates

Â in the UK went from 15% to less than 6%.

Â That's a staggering fall.

Â And this is been accompanied by an increase in the bond

Â index from a value of 95 to a value of just under 120.

Â And in general, we have this very good correlation, almost perfect I would say,

Â between short term interest rates and the performance of the bond market.

Â 2:40

We can illustrate this relationship between the yield and

Â the performance of the bond market by this chart here.

Â All these little dots, give you one observation.

Â And here we're back with the U.S.

Â between the starting yields of a government bond in the U.S.,

Â a ten year bonds, and the performance five year hence.

Â So over the next five years, what is the message here?

Â Well the message is that,

Â if you buy a bond when the initial yield is high, the probability

Â that this year will actually fall over the next five years say, is quite high.

Â So it means that, the probability that you will generate good returns with the bonds,

Â and this is the key thing to know, is high.

Â Conversely, when bond yields are low, as they are today.

Â Today, as we speak, the bond yield in the U.S. is 2.2%.

Â This is extremely low.

Â If you look at this chart, it doesn't even stand on the chart.

Â You see all these observations here?

Â Basically, the first one here of this period, starts at something like 3.5%.

Â So 2.2 is not even on the chart.

Â It's off the [LAUGH] the curve here.

Â So what do we mean by that?

Â 4:17

low probability that you will make high returns if you invest with bonds today.

Â Why is that?

Â Because the bond yield is low, so the probability that this bond

Â yield will increase overtime is actually quite high.

Â And we saw, already by now you should know, what should you know?

Â That when bond yields,arise, bond prices fall.

Â 4:44

One concluding remark with this chart, on the vertical axis here,

Â I've shown the real interest rates per year.

Â Over the next five years, so real meaning the nominal rate less the inflation rate.

Â So it's actually the true performance which you generate after inflation.

Â 5:06

So, now let's go back to the yield curve, and see how it moves

Â depending on what the central bank does by changing interest rates.

Â Here you see these two lines.

Â The blue line is the yield curve of the U.S.

Â bond market in December 2013.

Â And the yellow line is that same yield curve, but

Â just after the Federal Reserve tighten interest rates,

Â and this was done very recently, in December of 2015,

Â and we see that actually, the year curve has flattened.

Â It was quite steep.

Â You see the difference between 30 year bonds and 1 month interest rates

Â was just under 4%, or 400 basis points as we say.

Â Okay, this was in 2013.

Â And now, the difference between 30 bonds and

Â 1 month interest rates is 3% less 0.25%.

Â So just under roughly 2.775%.

Â So the yield curve has flattened.

Â Why is that?

Â Basically, what we say here is that by raising interest rates,

Â 6:36

It says, I bring interest rates because I anticipate that the better

Â economic environment in which we are in, will not translate into future inflation.

Â So basically, by doing this increase in interest rates, they lead

Â bond investors to believe that inflation will be lower in the future.

Â So they lower inflation expectation.

Â And this is why long term interest rates kind of ease a little bit.

Â So normally, we have that when interest rates go up, the year curve flattens.

Â Interest rates increase more at the shoulder end of the year curve than at

Â the long end, because by doing so, the Central Bank eases inflation expectations.

Â When this happens i.e., the yield curve flattens,

Â when short term interest rates increase.

Â We say that the Central Bank is ahead of the curve.

Â It's actually successful in keeping inflation expectations at the bay.

Â 7:51

So, now lets see what you can do with the duration,

Â when there are changes in the yield curve.

Â Basically as you remember, the duration is the key concept for

Â bond portfolio because it's the measure of the sensitivity

Â of your bond portfolio to change as an interest rate.

Â The higher the duration and remember here,

Â we put the formula here on the screen again.

Â The higher the duration,

Â the greater the sensitivity of your bond portfolio to changes in interest rates.

Â 8:38

Normally, if we have a flattening of the yield curve, you should increase duration.

Â Why is that?

Â Well, let's look at these two charts here.

Â We see that the yield curve may be flattening in two instances.

Â Let's start by the one on the right.

Â You see that if we start from year curve 1 and interest rates actually are reduced,

Â they may even reduce a bit further, a bit more, at the long end of the year curve.

Â So you see that the difference between long-term interest rates and

Â short-term interest rates, is actually reduced here, but

Â it can also happen if Central Bank, and this is normally what happens,

Â tighten monetary policies, increases short term rates, and

Â the long end of the yield curve actually also increases, but by less.

Â So there too, the year curve flattens.

Â So what you want to do here.

Â 9:38

Is you want to, as we say go short at the short end of the year curve,

Â and long, at the long end of the year curve.

Â Why is that?

Â Well take a look at the chart on the right.

Â You see that the arrow here,

Â the movement on the right of the far end of the year curve is quite big.

Â So basically, when you are position there,

Â when your bond portfolio is very long in duration,

Â then this where you capture the most dramatic fall in the yield.

Â So the best way to capture this dramatic fall of the long-term interest rate,

Â you capture it if you increase duration toward maybe the maximum.

Â Basically, here,

Â when we have this flattening of the yield curve, we say bullish flattening.

Â Because interest rates are coming down, and

Â you benefit the most from this falling interest rates.

Â If you position yourself, the duration of your bond portfolio, to the maximum here.

Â So, here the message is that, you should avoid or go short, short on bonds.

Â And you should pile into long term bonds and

Â increase duration to benefit from this movement.

Â 10:56

On the other hand, we have that the year curve may be steepening.

Â And this may happen in two instances.

Â If, as we have just seen the Central Bank is what we say,

Â how we say behind the curve.

Â It's increasing interest rates, but the bond market

Â is still believing that there is more inflation to come down the road.

Â So the Central Bank is behind the curve, it's not tightly

Â monetary policy fast enough, so inflation expectation keeps on growing, so

Â long term interest rates actually increase by more than short term interest rates do.

Â This is what we call bearish steepening.

Â Bearish because, bares means that the price of your bonds go down

Â because interest rates go up, and also there's the steepening of the yield curve.

Â The slope actually increases, but

Â it can also be a bullish steepening that's the chart here on the right, and

Â here, we have that the Central Bank is conducting a very aggressive,

Â easy monetary policy, and the long end of

Â the U curve decreases, but by less, so we have a steepening of the U curve.

Â So here, what you want to do is you want to decrease duration.

Â Why?

Â Because, and you see this from the best from the chart on your right.

Â That's where interest rates fall the most,

Â because interest rates fall the most at the short end of the yield curve.

Â So if you decrease duration, that's where you will capture the most,

Â this dramatic fall in interest rates.

Â So in conclusion, we saw that very mechanically,

Â where this formula of the net present value,

Â bond returns are good when interest rates go lower and conversely.

Â And we saw with this twists of the yield curves, that it may be steepening,

Â it may be flattening, depending on what inflation expectation do,

Â in relation to the conduct of monetary policies.

Â Basically, you should use your duration to adjust your bond portfolio,

Â 13:10

depending on what you think is going to happen to interest rates and

Â the shape of the year curve.

Â But generally, the whole very simple idea to put it very simply

Â is, when you expect the Central Bank to ease monetary policy.

Â So interest rates do go down, basically, you should increase duration

Â because you will tend to benefit with your bonds of these low interest rates.

Â And conversely, when you think that the Central Bank is going to

Â increase interest rates, you want to generally speaking, but

Â then it depends on the movement of the yield curve as we've seen, but

Â generally speaking, you want to reduce the duration,

Â because higher interest rates will hurt the returns of your bond portfolio.

Â [MUSIC]

Â