0:17

We use actually the same formula or

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

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

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

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

and the principal which you get back at the end.

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

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

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

Okay?

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

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

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

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

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

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

LIBOR meaning London Interbank Overnight Rate.

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

that, an inverted rating scale, in blue.

Why do I do this inversion?

Because, well, by now you know,

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

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

You see for instance, between '90 and

the 94 the short term interest rates

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

That's a staggering fall.

And this is been accompanied by an increase in the bond

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

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

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

2:40

We can illustrate this relationship between the yield and

the performance of the bond market by this chart here.

All these little dots, give you one observation.

And here we're back with the U.S.

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

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

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

Well the message is that,

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

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

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

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

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

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

This is extremely low.

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

You see all these observations here?

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

So 2.2 is not even on the chart.

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

So what do we mean by that?

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

Why is that?

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

yield will increase overtime is actually quite high.

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

That when bond yields,arise, bond prices fall.

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

I've shown the real interest rates per year.

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

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

5:06

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

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

Here you see these two lines.

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

bond market in December 2013.

And the yellow line is that same yield curve, but

just after the Federal Reserve tighten interest rates,

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

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

It was quite steep.

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

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

Okay, this was in 2013.

And now, the difference between 30 bonds and

1 month interest rates is 3% less 0.25%.

So just under roughly 2.775%.

So the yield curve has flattened.

Why is that?

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

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

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

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

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

So they lower inflation expectation.

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

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

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

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

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

when short term interest rates increase.

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

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

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

when there are changes in the yield curve.

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

bond portfolio because it's the measure of the sensitivity

of your bond portfolio to change as an interest rate.

The higher the duration and remember here,

we put the formula here on the screen again.

The higher the duration,

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

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

Why is that?

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

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

Let's start by the one on the right.

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

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

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

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

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

tighten monetary policies, increases short term rates, and

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

So there too, the year curve flattens.

So what you want to do here.

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

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

Why is that?

Well take a look at the chart on the right.

You see that the arrow here,

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

So basically, when you are position there,

when your bond portfolio is very long in duration,

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

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

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

Basically, here,

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

Because interest rates are coming down, and

you benefit the most from this falling interest rates.

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

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

And you should pile into long term bonds and

increase duration to benefit from this movement.

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

And this may happen in two instances.

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

how we say behind the curve.

It's increasing interest rates, but the bond market

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

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

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

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

This is what we call bearish steepening.

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

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

The slope actually increases, but

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

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

easy monetary policy, and the long end of

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

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

Why?

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

That's where interest rates fall the most,

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

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

this dramatic fall in interest rates.

So in conclusion, we saw that very mechanically,

where this formula of the net present value,

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

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

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

in relation to the conduct of monetary policies.

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

13:10

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

the shape of the year curve.

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

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

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

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

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

increase interest rates, you want to generally speaking, but

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

generally speaking, you want to reduce the duration,

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

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