[00:17] Okay, so let me let me continue with the
[00:20] the topic of the previous lecture, which
[00:21] is asset pricing.
[00:23] And we said the the tricky thing with
[00:25] asset pricing is that
[00:27] the payoff
[00:28] of having an asset comes in the future.
[00:31] And that that that implies
[00:35] at least two things.
[00:36] The first one is that
[00:38] we need to have a method to value
[00:41] returns in the future
[00:43] as of today.
[00:44] Okay? So, what is the equivalent to?
[00:46] After all, if you want to buy a
[00:47] financial asset, you need to pay for it
[00:49] today with dollars of today, and you are
[00:52] expected to receive some payoff in the
[00:54] future. You need to be able to compare
[00:56] these two things.
[00:58] And the second is that is related is
[01:00] that because this payoff is in the
[01:02] future, you need to have expectations
[01:05] about it. Okay? So, those are the two
[01:07] concepts
[01:08] we play with.
[01:09] Um
[01:10] and and the and and there's a third
[01:12] related concept, which is because it
[01:15] comes in the future, many things can
[01:17] happen in between, and so there's also a
[01:19] concept of risk. Okay? Those are the
[01:21] three
[01:22] elements we discuss.
[01:24] And
[01:25] remember we did I'm going to go very
[01:27] quickly over what we did in the previous
[01:28] lecture because I could see some faces.
[01:31] Uh so so let me go quickly over that and
[01:34] then then continue with equity, uh which
[01:36] was the next step. Um
[01:40] So, the first step was says, "Okay,
[01:42] ignore the expectations part for now and
[01:44] risk and so on. Assume that you know the
[01:46] future." And we ask the question,
[01:49] uh well, how do we value a dollar next
[01:51] year?
[01:52] Uh and in particular, do we want the
[01:54] question, is it equivalent to having a
[01:56] dollar today?
[01:57] And the answer quickly became no because
[02:00] imagine that you had the dollar today,
[02:01] then you can invest it for a year and
[02:05] you get the return of the
[02:06] the one-year interest rate return.
[02:08] So, with $1 today, you can do more than
[02:11] with $1 in the future.
[02:13] In fact, that calculation
[02:16] gave us the exact recipe to
[02:19] valuing a dollar in the future because
[02:22] in order to get a dollar in the future,
[02:24] I don't need a dollar today. I need one
[02:25] over one plus the interest rate.
[02:28] Uh I invest this in in the one-year
[02:31] bond, uh and and I get a return of that
[02:35] over that amount, that gives you exactly
[02:37] a dollar in the future. Okay? So, that
[02:39] gives us a very natural way of valuing a
[02:42] dollar next year, it's just one over one
[02:44] plus the interest rate. And by the same
[02:46] logic, if I have a dollar today and I
[02:48] want to invest it for two years, well,
[02:51] I'm going to earn that interest rate for
[02:53] the first year, and then I'm going to
[02:55] learn that earn that interest rate on
[02:57] the full product, not not on the
[02:59] original dollar, in the on the one plus
[03:02] IT dollars, I'm going to
[03:04] earn one plus IT plus one.
[03:07] And and and so I can generate sort of a
[03:10] lot of
[03:11] you know, if the interest rate is 10% on
[03:13] average, a dollar today generates 1.21
[03:17] uh dollars two years from now. So, that
[03:19] tells you by the same logic that one
[03:22] over 1.21 dollars
[03:24] uh
[03:25] today is equivalent to $1 in the future.
[03:28] Okay?
[03:29] So, then we said, "Let's pick a very
[03:32] general asset, an asset that has you
[03:34] know, that pays
[03:35] ZT dollars
[03:37] uh this year, then ZT plus one dollars
[03:41] one year from now, ZT plus two dollars
[03:43] two years from now, and so on and so
[03:45] forth up to n years ahead. Uh well, what
[03:49] is the value of that asset today? Well,
[03:51] you apply exactly the same logic that we
[03:52] apply here for every single uh year in
[03:56] the future,
[03:57] and you get that's that's the the Let's
[04:00] call the present present discounted
[04:01] value
[04:02] uh
[04:03] of those cash flows, that gives you the
[04:06] value today. Okay? Present discounted,
[04:08] those are the discount factors, one over
[04:11] and then that's the value that you get
[04:12] out of that. So, that asset
[04:15] has that present discounted value of uh
[04:18] future cash flows,
[04:20] and uh
[04:21] and uh
[04:23] that should be more or less the price
[04:24] that you are willing to pay for that
[04:26] asset. Okay?
[04:29] Uh and then we introduce expectations
[04:32] and okay, well, but we're talking about
[04:33] cash flows in the future, in many cases,
[04:35] we don't know. Well, we don't know two
[04:37] things. First, we don't know
[04:39] what the cash flows may be.
[04:41] In a very safe bond, you do know the
[04:43] cash flow, but but but almost any other
[04:47] asset, you don't know exactly the cash
[04:50] flows you receive, and you don't know
[04:52] what the future interest rates, one-year
[04:55] interest rate will be.
[04:56] Okay?
[04:57] So, that took us to the concept of
[04:59] expected present discounted value, in
[05:01] which you just replace all the things we
[05:04] don't know today for the expectations of
[05:06] those things. Okay? So, we don't know
[05:08] the cash flows in the future, that's the
[05:09] reason
[05:10] but we have an expectation,
[05:12] that's that's what you put there, and uh
[05:25] we don't know the future we know the
[05:26] current interest rate, but we don't know
[05:27] the less
[05:28] than it was when the interest rate was a
[05:30] little lower. Okay?
[05:32] Okay, and then we look at a two-year
[05:34] bond, a bond that pays nothing up to two
[05:36] years from now, and we said, "Well, two
[05:38] years from now pays 100 and then
[05:40] matures." Well, the price of that bond
[05:42] will be
[05:44] you know, this. Okay? And notice that in
[05:47] this case, the price of a two-year bond
[05:49] at time t goes down if the either of the
[05:52] one-year rates goes up. Okay? It can be
[05:55] the first this year's one-year rate, or
[05:59] then maybe that's the expectation that
[06:00] the one-year rate uh
[06:03] next year will go up. Okay?
[06:07] Good.
[06:08] Then I introduce an important concept,
[06:10] which is this concept of arbitrage
[06:12] pricing.
[06:13] Okay? Which is
[06:16] uh two instruments
[06:18] uh
[06:19] um
[06:21] should give you sort of the same
[06:22] interest rate. We're leaving risk
[06:23] considerations aside. It should give you
[06:25] the same return
[06:27] when you compare them
[06:29] uh um
[06:31] uh over the same maturity. Okay? So,
[06:35] in this particular example, I said,
[06:37] "Look,
[06:38] a one-year bond
[06:40] and a two-year bond that you invest you
[06:42] hold for only one year should give you
[06:45] more or less the same return."
[06:47] Okay?
[06:48] So so
[06:49] so that means
[06:52] that
[06:53] this is the return you get from a dollar
[06:55] invested in a one-year bond,
[06:58] okay? Should be equal to the return you
[07:01] get
[07:02] by investing in a in a two-year bond and
[07:04] selling that bond after one year.
[07:07] And that's the expression we had here.
[07:10] Okay?
[07:11] If you this is what you pay for a for a
[07:13] for a two-year bond, and this is what
[07:16] you expect uh uh
[07:19] to to be paid for that bond when you
[07:21] sell it one year from now. Notice that
[07:24] one year from now, the two-year bond
[07:26] will
[09:55] when you sell it 1 year from now. Notice
[09:57] that 1 year from now the 2-year bond
[09:59] will be a 1-year bond because 1 year
[10:02] will have expired and that point it will
[10:03] be a 1-year bond. That's the reason we
[10:05] have a subscript P1T here.
[10:08] So, that means that we can solve from
[10:09] here that P2T is simply that.
[10:13] But there's an expression like the one
[10:15] we had for the 1-year bond at time T,
[10:17] there is 1 over T plus 1. We put
[10:19] expectations because we don't know the
[10:21] actual interest rate in the future.
[10:25] And then I stuck this into there and I
[10:29] we got exactly the same price that we
[10:32] got with the net present expected
[10:34] present discounted value approach, okay?
[10:36] And so, this asset pricing this
[10:38] arbitrage way of pricing things is an
[10:40] incredibly powerful tool
[10:42] that is used very extensively in
[10:43] finance. This These are simple
[10:45] calculation, but when assets gets to be
[10:47] tricky, much more complicated,
[10:50] this is is very useful.
[10:54] Then we talk about bond yields.
[10:57] And bond yields are defined
[11:00] as the constant interest rate
[11:03] that
[11:06] that is consistent with the current
[11:08] price of that particular bond.
[11:11] Okay? So, in the case of the 2-year bond
[11:14] we call the 2-year rate.
[11:16] That interest rate that is constant over
[11:19] the two periods.
[11:21] That's Okay, that's the reason I have
[11:22] squared it. It's not I1T * 1 I1T + 1.
[11:27] I squared it.
[11:29] It's not constant over time. This The
[11:31] 2-year interest rate may be moving a
[11:32] lot. I mean, the the Fed just hiked by
[11:34] 25 basis points. I'm sure all rates are
[11:36] moving at this moment. So, the rates can
[11:38] be moving at all points in time, but
[11:41] they But we define as the yield is at
[11:42] one point in time. You tell me the price
[11:44] of the bond. You tell me the payoff of
[11:46] the bond, then what is the the the
[11:49] constant interest rate that makes this
[11:52] price this expression equal to the
[11:54] actual price? That's the way we define
[11:57] the 2-year rate. That's the 2-year rate.
[12:00] And if you have a bond that pays 100 n
[12:03] years from now, then there would be a
[12:05] constant interest rate In n, you know,
[12:08] that that gives you 100 divided by 1
[12:11] plus InT
[12:13] uh
[12:14] to the n
[12:15] to the n power
[12:17] that will give you
[12:19] that you set that equal to the price the
[12:22] actual price of the bond, the one you
[12:24] get out of expected present discounted
[12:26] value or out of arbitrage, then you have
[12:29] found the yield or the yield to
[12:31] maturity.
[12:34] You know, we know what the We already
[12:36] got the price from the previous slide.
[12:38] We know that the price of this bond is
[12:39] going to be 100 as a 2-year bond
[12:42] divided by this product of 1 plus
[12:44] interest rate 1-year interest rate. So,
[12:47] this has to be equal to that. That's the
[12:48] way actually you calculate the 2-year
[12:50] yield.
[12:52] Uh
[12:52] and numerators are the same, that means
[12:54] the denominators have to be the same.
[12:56] And this implies approximately that the
[12:59] 2-year rate is a sort of average of the
[13:02] expected 1-year rate, okay?
[13:05] So, in this case the 2-year rate is a
[13:08] sort of average of the 1-year rate. That
[13:10] means that when the
[13:12] when you expect the interest rate to be
[13:15] the 1-year rate to be rising over time
[13:17] then the 2-year rate will be above the
[13:19] 1-year rate today.
[13:21] That's when the curve is We say the
[13:23] curve the yield curve is steep. Let me
[13:25] show you something.
[13:31] There.
[13:33] When the curve looks like that, so steep
[13:36] means that
[13:38] the the the later the 2-year rate the
[13:41] 3-year Well, here in particular the
[13:43] 3-year rate is the 2-year rate is higher
[13:45] than the 1-year rate. The 3-year rate is
[13:48] higher than the 2-year rate and so on
[13:49] and so forth.
[13:50] That happens when when you expect the
[13:54] market expects the interest rate to be
[13:55] rising
[13:56] over time. The 1-year rate to be rising,
[13:59] okay? Because Remember the 2-year rate
[14:02] is the average of the existing the
[14:04] current 1-year rate plus the expected
[14:06] 1-year rate 1 year from now.
[14:08] For that average to be higher than the
[14:10] 1-year rate now, it has to be the case
[14:13] that the one expected 1-year rate 1 year
[14:15] from now has to be higher than the
[14:17] current 1-year rate. Okay? So, that's
[14:20] what you tend to get uh
[14:22] that's when you get to the upward
[14:23] sloping term structure. And when you get
[14:25] a downward sloping term structure, which
[14:27] is the way it looks right now, actually
[14:29] right now looks very downward sloping.
[14:31] There you are. You know, it looks very
[14:32] downward sloping. Is people expect that
[14:35] we're getting to the peak of current
[14:38] policy rate of short-term interest rate.
[14:40] And so, people expect now for the
[14:42] interest rate to decline going forward.
[14:45] And that's the reason
[14:46] the the the 2-year rate now is lower
[14:50] than the 1-year rate.
[14:53] And the 5-year rate is lower than the
[14:55] 2-year rate and so on.
[14:59] Uh as you can see here, it's very steep.
[15:02] Okay. Then we said, "Well, let's add
[15:05] risk because here Sure, here we assume
[15:08] that you were indifferent between
[15:10] investing in a completely safe 1-year
[15:12] bond
[15:13] and a and a 2-year bond in which you
[15:15] have to make an expectation about the
[15:17] price, but that price could move around.
[15:18] So, there's risk on that price or the on
[15:20] the price of 1-year
[15:22] bond the 1-year bond
[15:25] uh
[15:25] as of today.
[15:27] And then and so
[15:31] So, we added risk. And there are two
[15:33] type of risk in bonds. One is default
[15:35] risk that, you know, that that they had
[15:37] promised they would pay you 100, but it
[15:39] may it may be happen that they cannot
[15:41] pay you the 100. The corporation or the
[15:43] government or so on. Argentina defaults
[15:45] in its bonds regularly, okay?
[15:48] Uh for example. Uh
[15:50] many of the of the of the
[15:53] regional banks that had gone under will
[15:54] default on their bonds as well, okay?
[15:57] So, that kind of risk. But we remove
[15:59] that risk and we'll focus for now on the
[16:01] I'm going to focus mostly on the price
[16:02] risk because I'm going to be talking
[16:04] mostly about US Treasury bonds. US
[16:06] Treasury bonds have no default risk, we
[16:08] think. I mean, there could be an event
[16:10] in a few weeks from now, but no one
[16:13] expects that to be a lasting event. I
[16:15] mean, if it is, there's a real mess, but
[16:18] But anyway, but there is also price risk
[16:20] because you have to hold this and then
[16:22] sell it at the end of 1 year and you
[16:24] don't know exactly the price what the
[16:25] price will be. Okay? There's a risk
[16:27] associated to that.
[16:29] So, so that means that really you
[16:32] shouldn't equalize the return on the
[16:34] 1-year bond to the return you expect to
[16:37] get in in the 2-year bond. You should
[16:40] add a little compensation for holding
[16:42] the 2-year bond, for going the 2-year
[16:44] bond route, okay? And so, rather than
[16:47] expect to make 1 plus I1T
[16:50] uh
[16:51] with with the 2-year bond after 1 year,
[16:54] you should expect to earn a little more,
[16:56] okay?
[16:57] And that's what this XB being positive
[17:00] reflects. And so, in that case the price
[17:03] the price of the 2-year bond is a little
[17:05] different from what we had. In fact,
[17:07] it's a little lower than what we had
[17:09] because that's the way you compensate
[17:10] for risk. I sell you an instrument a
[17:12] little cheaper than it would have been
[17:14] in the absence of risk,
[17:16] so you you expect to get a little a
[17:18] slightly higher return out of that,
[17:20] okay? So, this price is lower than the
[17:23] price without the risk premium here.
[17:26] No? That means but it's still is
[17:28] promising you 100, so that's exactly how
[17:30] you get more return out of it because
[17:32] you were buying something at a lower
[17:33] price.
[17:34] Okay?
[17:43] So, I can do the same logic now and see
[17:46] what the 2-year rate is, but now that I
[17:49] have this
[17:50] taking to account this risk and you have
[17:52] that the 2-year rate now is the average
[17:55] not only of the expected 1-year rate,
[17:57] but also includes a risk premium.
[18:00] Okay?
[18:01] And so, and that tends to be the case
[18:03] that the the further out in the curve
[18:05] you are, the larger is that risk
[18:06] premium. It's called term premium
[18:09] because term is the same as maturity,
[18:11] okay?
[18:13] Um
[18:16] Actually
[18:18] sometimes that that is negative,
[18:20] actually.
[18:21] May and and recently up to very
[18:23] recently. Now it's positive. But until
[18:25] very recently that XB was negative.
[18:28] And the reason for that, you don't need
[18:29] to understand that now, is because
[18:32] long-term bonds were great hedges.
[18:35] Uh meaning meaning, you know, if there
[18:37] is a for any major event, for a
[18:39] financial crisis or something like that,
[18:42] because in a financial crisis or a major
[18:44] disaster
[18:46] interest rates tend to fall.
[18:49] And when interest rates fall, the price
[18:50] of bonds go up.
[18:52] Okay? And and so so that was a good
[18:55] hedge. If you wanted to to protect your
[18:57] your portfolio of equities and so on
[18:58] against a major catastrophic major event
[19:02] like a financial crisis or, you know, a
[19:04] war or something like that, it was not a
[19:06] bad idea to have some long-term US
[19:08] Treasury bonds in your portfolio because
[19:12] they would tend to go up precisely when
[19:14] everything else was going to be losing
[19:16] money, okay? And so, that's the reason
[19:17] tend to be negative. Now that's not the
[19:19] case because now one of the biggest risk
[19:21] is inflation.
[19:23] And so so uh if there's an inflationary
[19:26] spike,
[19:27] then interest rate will go down up, not
[19:29] down. And that means the price of bonds
[19:31] will decline. So, they will decline at
[19:33] the wrong time,
[19:35] So, the price of bonds of long-term
[19:36] bonds now will tend to decline
[19:38] uh when everything else is also
[19:40] plummeting. I mean, if we get a negative
[19:42] if we get an inflation surprise that
[19:43] inflation is a lot higher than people
[19:45] expected, asset prices are going to
[19:47] decline, all of them, including
[19:49] long-term bonds. And that's the reason
[19:51] now this XB is positive.
[19:56] Okay, so that's I think that's where we
[19:58] were at in the previous lecture.
[20:01] Any questions about that? Then I'm going
[20:02] to Next step is to talk about equity.
[20:06] No?
[20:07] Yeah.
[20:08] Why don't we add the interest the risk
[20:10] to the interest rate for the one year
[20:12] now?
[20:15] Well, because next year that one for
[20:17] this particular bond
[20:19] that that bond will have no risk because
[20:23] it will be one year to go
[20:25] and at the end of that year you're going
[20:26] to get the 100.
[20:28] So, there's no risk that added. If it
[20:30] was a three-year bond, then you would
[20:32] have in two of those you would have risk
[20:35] premium.
[20:36] And but you wouldn't have it in the last
[20:37] one because in the last one you don't
[20:38] have the you're going to receive the
[20:40] 100.
[20:42] If the bond could could could default
[20:45] so because I'm only looking at price
[20:47] risk in the bond.
[20:48] Uh uh
[20:49] if the bond could could default, then I
[20:52] would add an extra
[20:54] term there because it's the fall risk.
[20:56] But but here I'm just looking at price
[20:58] risk and I'm assuming the the unit of
[21:00] time is one year. So, just one year
[21:03] before it expires there's no more risk
[21:05] because there's no price in between
[21:07] and and you're going to receive a 100
[21:10] uh uh
[21:11] at the end of the year. In reality
[21:14] time is continuous. So, so every second
[21:16] there's a little bit of a risk. So, you
[21:17] have a little bit of that risk all the
[21:19] time except for the last second.
[21:21] Uh but but
[21:23] I'm looking at a simple example where
[21:24] you know
[21:26] things happen every one year. And
[21:31] In the book I think they mess up
[21:33] actually. They put the risk premium in
[21:35] the wrong place. But
[21:37] there was another question.
[21:40] No?
[21:41] Okay.
[21:44] So
[21:44] let's look at the stock prices now.
[21:47] Uh
[21:49] So, a stock price has two key
[21:50] differences with respect to
[21:53] um
[21:56] Well, certainly there were but two that
[21:57] I want to highlight.
[21:59] The first is that they don't pay
[22:01] coupons, fixed amount. They don't
[22:02] promise you to pay, you know, $100 two
[22:05] years from now or anything like that.
[22:07] They pay dividends.
[22:09] Okay?
[22:10] They tell you we have a policy of paying
[22:12] dividends and even different companies
[22:14] differentiate themselves by how much
[22:16] they promise to give you on average in
[22:18] dividends, but it's a promise that if
[22:20] everything goes as planned, they'll pay
[22:22] you those dividends.
[22:24] It's not a commitment to pay you a
[22:26] dividend. When it's very different from
[22:28] a bond. A bond says, "I'll pay you a
[22:30] coupon of this amount every six months."
[22:33] And if you don't pay that coupon, that's
[22:35] a default.
[22:37] There's nothing like that in equity.
[22:38] Equity you buy shares of Apple and you
[22:41] sort of look at the history of dividend,
[22:43] what what the CEO told you the last time
[22:45] the in the last release uh and and and
[22:49] you know, you you can you you think,
[22:50] "Okay, these are more or less going to
[22:51] be my dividends." But there's no
[22:52] commitment.
[22:55] They will always tell you
[22:57] what's their plan
[22:58] but it's a plan. It's not a commitment.
[23:00] So, that's the first thing. It doesn't
[23:01] have fixed coupons or anything like
[23:03] that. There's no commitment. And in that
[23:05] sense there's no sense of default
[23:07] because there was no commitment, so
[23:08] there's no default.
[23:10] Uh if if a company has to cut dividends
[23:13] to zero, that's not a default.
[23:15] That's
[23:16] conditions change. That's it. There was
[23:17] no commitment to that.
[23:20] The second
[23:21] feature is that they don't have a fixed
[23:23] terminal date.
[23:25] 99.9999999%
[23:28] of the bonds do have a terminal date.
[23:29] They have a maturity. I mean, there's a
[23:31] few exceptions which are called
[23:32] perpetuities.
[23:34] That I think the US has none for
[23:36] example. But but but but most bonds have
[23:39] a
[23:40] uh uh a a maturity.
[23:42] Okay?
[23:44] Equity doesn't come that way. Nobody
[23:46] tells you buy a share of Apple you don't
[23:47] buy shares of Apple that
[23:50] they will that will be retired 30 years
[23:52] from now. Okay?
[23:54] They will be there as long as Apple's
[23:56] exist.
[23:57] Okay?
[23:58] Uh
[24:00] Now, of course, you know, if you had
[24:02] shares of First Republic Bank, you have
[24:04] nothing now.
[24:05] And because of that but but that was not
[24:07] the original plan. If First Republic
[24:09] Bank had been successful, you would have
[24:12] the the shares would have survived for a
[24:13] very long period of time. Okay?
[24:15] So so there's no sense of maturity. In
[24:18] principle
[24:19] equity can last forever.
[24:22] Okay?
[24:27] So, I'm going to use arbitrage to to to
[24:30] price equity.
[24:33] So
[24:34] uh
[24:35] let me So, let's we have the following
[24:37] uh
[24:38] portfolio of options here.
[24:40] Uh
[24:41] one is our old one-year bond.
[24:44] Okay? So, you can invest your dollar
[24:45] today in a one-year bond.
[24:48] The alternative I'm going to say there
[24:49] is some equity out there. And I'm going
[24:51] to call the price of that equity Q
[24:55] and the dividend of that e- e-
[24:57] equity D. Okay?
[25:01] So
[25:03] so let's price this stock by by
[25:06] arbitrage. So
[25:07] equity is risky.
[25:09] I mean, that is much riskier than than
[25:12] than than bonds unless you are into
[25:14] Argentinian bonds or things like that.
[25:16] But I mean, it's much riskier than
[25:17] bonds.
[25:18] So, there's always a risk premium and
[25:20] actually that itself is a trade. You
[25:22] trade the risk premium of equity market.
[25:25] So, I'm going to put an XS here. So what
[25:28] do you what do you expect to get from
[25:30] from holding
[25:31] Remember, arbitrage means the same
[25:33] holding period. So, I'm going to compare
[25:35] investing in a one-year safe bond
[25:39] versus
[25:41] buying equity today, buying a stock
[25:44] holding it for a year
[25:46] and then selling it there.
[25:48] Okay? That because that's That's I
[25:50] cannot do arbitrage for paying different
[25:52] holding periods. That's a one-year
[25:54] holding period.
[25:55] So, I'm saying this is what I'm going to
[25:57] get from the bond. I'm going to require
[25:59] some risk compensation for that because
[26:01] risk equity is risky. So, I'm going to
[26:03] want that. And this is what I'm going to
[26:05] get That's my return on equity I get.
[26:07] This is what I'm going to pay today for
[26:09] the stock
[26:10] say for a share of Apple
[26:12] and I'm going to get this. This is the
[26:13] dividend I expect to get
[26:16] at the end of the year
[26:18] and then I this is the price at which I
[26:19] expect to sell
[26:21] that share
[26:23] one year from now.
[26:24] Okay?
[26:25] So, that's the return I'm expecting to
[26:27] get from holding the share of Apple for
[26:30] one period.
[26:31] Okay?
[26:32] And that's what I need to compare with
[26:33] holding for one year
[26:35] one-year bond. But I want also to be
[26:38] compensated uh
[26:40] for uh
[26:42] risk. Okay?
[26:44] Good.
[26:47] Is this clear?
[26:51] Okay,
[26:51] good.
[26:53] I don't know whether silence means yes
[26:54] or no. But this is
[26:56] No, we did something like this with the
[26:57] two-year bond except that we didn't have
[26:59] a a dividend there, you know,
[27:02] because there was no coupon at day one.
[27:04] We only had a final payment of 100. But
[27:07] we did this already when we compare the
[27:09] one-year bond with holding the two-year
[27:11] bond for one period. We had exactly that
[27:14] except that there was the expected
[27:15] dividend there was zero because there
[27:17] was no payment at the intermediate date.
[27:20] Okay?
[27:22] Good. So, we we know this concept
[27:23] already. The only difference here is
[27:25] again that there is expected dividend
[27:27] and second that we have a risk premium
[27:31] here which we added for bonds, but for
[27:32] equity as I said it's typically much
[27:34] larger than for bonds, especially if
[27:36] you're talking about treasury bonds.
[27:41] So, I'm going to reorganize this to
[27:43] solve out for the price, this QT here.
[27:45] That's what I want to figure out. What
[27:46] is the price of the share of Apple?
[27:48] Okay?
[27:49] Well
[27:50] I can reorganize this which means, you
[27:53] know, move
[27:54] dollar QT to the left, divide these two
[27:57] guys here by 1 + I1T + XS and I get
[28:00] this. Okay?
[28:02] So, the price is equal to
[28:05] the discounted
[28:07] expected dividend. I have to discount it
[28:09] because I expect to receive it one year
[28:11] from now and I want I also compensation
[28:13] for risk
[28:15] plus the discounted value of the
[28:19] money I'm going to get from from selling
[28:20] the share of Apple one year from now.
[28:23] Okay? Which I also discount
[28:25] by the interest rate, but also with a
[28:27] risk premium because that's a risky
[28:28] investment.
[28:30] Okay?
[28:31] So, that's what we have.
[28:34] Now
[28:36] notice that
[28:39] at T + 1
[28:42] I will have an expression like that as
[28:44] well.
[28:46] Okay, again.
[28:48] When we did the two-year bond
[28:50] we didn't have an expression like that
[28:52] because
[28:54] after after one year the two-year bond
[28:56] was going to be a one-year bond.
[28:58] And so, we didn't need to think of put a
[28:59] price there. We just put the 100. Okay?
[29:02] Here is different because we said this
[29:04] equity never expires unless the company
[29:06] goes bankrupt, it's there.
[29:09] So, in the next date I'm going to have
[29:11] an expression exactly like that. I'm
[29:14] just going to have an expected T +
[29:16] dividend at T + 2 and expected price at
[29:19] T + 2. Okay? And so on and so forth.
[29:22] That means
[29:24] I can replace this expression here
[29:27] by an expression like this shifted all
[29:30] by one year.
[29:33] Okay? And I keep can keep doing that.
[29:36] Then if I do that, I'm going to get then
[29:39] two expected dividends here and then I'm
[29:41] going to get a
[29:42] uh So, I'm going to get
[29:44] something like this but shifted by one
[29:46] year and discounted by two terms in the
[29:49] denominator, and then I'm going to get a
[29:51] expected Q QT + 2.
[29:54] Around here, okay?
[29:56] Well, I can do a substitution of that as
[29:57] well. Again,
[29:59] okay? By everything shifted by two
[30:01] years, and so on.
[30:03] So, I can keep going.
[30:05] And I can keep going, and going, and
[30:06] going, and going on forever.
[30:08] Okay?
[30:09] So, if you keep doing it,
[30:11] you're going to end up with an
[30:12] expression that gives you the price of
[30:15] the asset as expected this
[30:18] present discounted value of all the
[30:19] future dividends you expect.
[30:22] Okay?
[30:24] You see? I I'm summing
[30:26] the T + 2, 3, 4, 5, and doesn't stop
[30:30] here.
[30:31] If I stop here, I'm going to have here a
[30:34] you know, a Q
[30:36] E T + N
[30:38] + 1.
[30:40] Well, I can replace that thing again,
[30:41] and I can keep going, keep going
[30:42] forever.
[30:43] Okay? So, you're going to integrate the
[30:45] expected dividends, discounted dividends
[30:48] to infinity.
[30:51] Now, each future dividend is discounted
[30:53] more and more heavily because the
[30:55] denominator is growing, and growing, and
[30:57] growing, because it's further out in the
[30:58] future, it's worth less and less. Okay?
[31:00] But, still it can go on forever.
[31:03] And in fact, even if you if you
[31:05] substitute this stuff a million times,
[31:07] there's going to still be a little price
[31:09] at the very end floating around.
[31:12] Discounted, but it will never go away.
[31:16] Okay? So, it never ends. There's no
[31:18] maturity.
[31:19] They keep going.
[31:22] Now, I did everything up to now for
[31:24] nominal in nominal terms. You can do
[31:28] And that's the reason I
[31:29] didn't want to spend much time with
[31:30] this. You can do everything in real
[31:31] terms as well.
[31:33] Uh
[31:34] and and and all all that happens here is
[31:35] just remove the dollars, and just be
[31:37] careful to replace uh
[31:41] the nominal interest rate by the real
[31:42] interest rate, but nothing deep there.
[31:44] Okay? I can you can go to real pricing,
[31:47] nominal pricing, and so on.
[31:50] Okay? But, the the important concept is
[31:52] not that. It is is the fact that
[31:55] this that the the in principle we call
[31:58] that, by the way, the fundamental value
[32:01] of a of a of a of equity or of stock is
[32:04] the expected present discounted value of
[32:06] all the dividends. And you have to
[32:08] discount it by the proper discounting
[32:09] factor, which includes interest rate and
[32:11] risk premium. But, that's what we call
[32:13] typically fundamentals. We differentiate
[32:15] that from what we call sometimes, I'm
[32:17] going to show you an example later on,
[32:18] bubbles.
[32:20] When when the price seems to exceed
[32:23] any reasonable sense of fundamentals.
[32:26] Okay?
[32:32] Okay, good.
[32:34] Okay, let me sort of start
[32:36] going back to to things that that um
[32:40] we worry about in this course, and in
[32:41] fact is a big issue. I don't know what
[32:43] is happening to markets now. The what
[32:45] the Fed did was very anticipated, but
[32:47] but
[32:48] um
[32:50] but markets of often find a way to react
[32:53] to things even if things were
[32:54] anticipated, but
[32:57] What happens? So, let me ask you a
[32:59] following question.
[33:01] What is the effect What do you think is
[33:03] the effect
[33:05] of an expansionary monetary policy
[33:08] on the asset prices we have discussed?
[33:09] So, bonds and equity.
[33:13] Let's start with bonds
[33:15] first.
[33:16] What do you think is the effect of an
[33:18] expansionary monetary policy? That means
[33:20] a reduction in the interest rate on the
[33:21] price of your 1-year bond, 2-year bond,
[33:24] any any year you pick.
[33:30] We already talked about that earlier.
[33:35] Goes up.
[33:36] The price of a bond is inversely related
[33:39] to
[33:41] the interest rate because if I cut an
[33:43] interest rate,
[33:44] means
[33:45] a bond is something that pays the payoff
[33:47] is in the future.
[33:49] That thing in the future is worth more
[33:52] if the interest rate goes down.
[33:54] There's less discounting of it.
[33:56] So, the price of the bond, any bond
[33:58] here, will go up. The 1-year, 2-year,
[33:59] 3-year, 5-year, all of them.
[34:02] They'll go up. Okay?
[34:04] Assuming that nothing changes as a
[34:06] result of the monetary policy. Look,
[34:07] what happens is sometimes,
[34:09] you know, markets think, "Oops, the Fed
[34:11] messed up." And that leads to lots of
[34:13] changes in all the term structure and
[34:14] things like that because
[34:16] they expect the market to react in a
[34:18] strange ways to to this mistake made by
[34:20] the Fed. But, here I'm saying suppose
[34:22] that the Fed just cuts the interest rate
[34:24] once, and everyone believes that the Fed
[34:25] will continue to do so, and so on.
[34:27] Well, then you're going to get uh that
[34:31] that the price of bonds will go up.
[34:34] What will happen to the price of stocks?
[34:38] You want to answer.
[34:41] Up.
[34:43] But, it's
[34:45] Well, but it's important to see that it
[34:46] will go up probably for two reasons.
[34:49] The first one
[34:50] is that that
[34:52] um
[34:54] is that
[34:55] it's also the case that a lot of the
[34:58] price of an equity, actually even more
[35:00] so than a bond,
[35:01] has to do with expected payoffs in the
[35:04] future.
[35:05] So, if I lower interest rate, just the
[35:06] effect of discounting will tend to raise
[35:09] the price of So, even if I don't change
[35:11] the expected dividends at all,
[35:13] the fact that the interest rate goes
[35:14] down,
[35:15] for the same reason that the price of a
[35:17] bond went up, the price of equity will
[35:19] tend to go up. Okay? So, that's exactly
[35:21] is the same logic.
[35:23] But, there's an extra kick here for
[35:25] equity, which is what?
[35:27] That bonds did not have,
[35:29] but equity does.
[35:31] At least if it is an equity that is
[35:33] positively related to aggregate
[35:35] activity, but that's what I'm assuming
[35:36] here.
[35:53] Well,
[35:55] yeah, that's the logic, no? Here, the
[35:57] expansionary monetary policy is cutting
[35:59] interest rate, but as a result of that,
[36:00] output is going up.
[36:02] When output is going up, sales will go
[36:04] up, revenues will go up, dividends will
[36:06] probably go up as well.
[36:08] So, monetary policy can have very large
[36:10] effect. I mean,
[36:12] people in financial markets are looking
[36:13] at the Fed all the time because it can
[36:15] have a big impact on the price of those
[36:18] assets.
[36:19] An equity in particular can can be very
[36:21] strong. And in fact, that's one of the
[36:23] ways monetary policy works.
[36:25] You know, when when when
[36:28] the Fed cuts interest rates,
[36:31] inflate it inflates the value of asset
[36:32] prices, and that creates more wealth,
[36:35] people feel richer, consume more, blah
[36:37] blah blah. Firms feel also richer, they
[36:40] invest more, and so on. That's That's it
[36:42] That's
[36:43] That's deliberate in a sense. Okay?
[36:45] Uh that's one of the main mechanisms
[36:47] through which monetary policy affects
[36:49] aggregate demand. Just creates wealth.
[36:52] And when there's too much demand too
[36:54] much aggregate demand, like last like is
[36:56] going on now, that's the reason we have
[36:57] inflation, and so on.
[36:59] You know, in 2022, the Fed went out and
[37:02] deliberately destroyed wealth.
[37:05] Because that's what that's what needed
[37:06] to. Raise interest rate a lot, the price
[37:08] of equity came down, even houses began
[37:10] to bubble. Okay? The price of
[37:13] uh of of treasury bonds also collapsed,
[37:16] and so on and so forth. Okay?
[37:19] Good.
[37:21] Another experiment that we did sort of
[37:22] early on, lecture three, four, but
[37:25] around there,
[37:26] is
[37:27] What happens What do you think happens
[37:29] when there's an increase in consumer
[37:30] spending?
[37:32] So, suppose that now, remember we had a
[37:34] a C 0 floating around, an autonomous
[37:36] consumption component, and so suppose
[37:39] that that goes up.
[37:43] What do you think happens to asset
[37:44] prices?
[37:47] And this is a big issue these days,
[37:48] actually.
[37:54] Exactly. That's right. That's That's
[37:56] That's very good. It depends a lot. I
[37:58] mean, when financial markets receive
[38:00] news every day, there are releases of
[38:02] news and of all sort of things. Okay?
[38:05] And and
[38:06] in financial markets, they people always
[38:08] think, "Okay, this is the news.
[38:10] The obvious thing for this is
[38:13] you know, good news, because this will
[38:14] tend to increase output. Output will
[38:16] increase dividends. That's a good good
[38:17] thing for
[38:19] for stocks."
[38:20] Uh
[38:21] But, the immediate reaction is, "Whoa,
[38:24] but what will the Fed do about this?
[38:26] Does the Fed like
[38:27] that we have more aggregate demand or
[38:29] not?"
[38:30] Okay?
[38:31] And so so so that's that's
[38:34] key here.
[38:35] And and uh so suppose that in this case,
[38:39] the Fed did not like
[38:41] the Fed like today to the Fed doesn't
[38:43] want more aggregate demand today.
[38:45] There's no central bank around the
[38:46] world, maybe in China, but but there's
[38:48] no other central bank around the world
[38:50] that wants more aggregate demand.
[38:53] Okay?
[38:54] So, so if if it's if if you the release
[38:57] is consumer
[39:00] are very bullish now,
[39:02] uh
[39:03] that's not good news. I mean, financial
[39:06] markets immediately say, "Uh-oh, we have
[39:08] a Fed that is watching for inflation.
[39:10] This means they're going to hike
[39:11] interest rates."
[39:12] Okay?
[39:13] So, what happens to the price of bonds
[39:15] then in this environment when C 0 goes
[39:19] up, and the Fed doesn't like it? And and
[39:21] the markets know that the Fed doesn't
[39:22] like it. The Fed may take a month to
[39:24] react to it, but markets react
[39:26] immediately, say, "Whoa, this is what
[39:28] the Fed will do 1 month from now."
[39:30] Okay?
[39:32] So, what do you think happens to the
[39:33] price of bonds
[39:35] if we get news that, you know, consumers
[39:37] are
[39:38] very bullish, and and and and it turns
[39:41] out that we also have
[39:42] of you know 4% or so, so we know that
[39:45] the Fed doesn't like more aggregate
[39:46] demand.
[39:48] What do you think will happen to the
[39:49] price of bonds?
[39:56] Well,
[39:58] again,
[39:59] the news happens say
[40:02] uh
[40:03] a week ago
[40:05] and the Fed moves one week later.
[40:07] So so markets are going to anticipate
[40:10] that in this case the Fed will hike
[40:11] interest rates.
[40:14] If the Fed is the markets anticipate
[40:15] that the Fed will hike interest rate,
[40:17] interest rate will go up immediately.
[40:19] Not the not the rate that the Fed
[40:21] controls, but the one-year rate, the
[40:22] two-year rate, the three-month rate, all
[40:24] those rates are going to go up
[40:25] immediately as a result of that.
[40:28] Okay? And that
[40:30] we know
[40:31] reduces the price of bonds. Bonds and
[40:33] interest rates are The price of a bond
[40:35] and the interest rates are inversely
[40:36] related. So the anticipation that the
[40:38] Fed will hike rate will lead to higher
[40:41] interest rates at all horizons and and
[40:43] and that will reduce the price of bonds.
[40:46] Okay? So this thing that and for equity,
[40:50] well, look what happened for equity
[40:52] here. Well, for equity you say, "Okay,
[40:54] well, I get the same discounting effect
[40:56] of the bond, which is bad news, goes
[40:58] down."
[40:59] And
[41:00] and what about The good news is the
[41:01] dividend, no? Because now I have more
[41:03] consumers.
[41:05] Well, that depends on how much the Fed
[41:07] dislikes this stuff because if the Fed
[41:09] does this, that mean it offsets it fully
[41:11] offsets
[41:13] the the effect on aggregate demand.
[41:16] Increasing this zero shift IS to the
[41:17] right, that would have increased output
[41:19] to here. The Fed doesn't want more
[41:21] output, so we will hike interest rate up
[41:23] to the point in which output doesn't go
[41:24] up.
[41:25] That means dividends are not going to go
[41:27] up either.
[41:28] So we get just a negative effect of the
[41:30] discounting and we don't get the benefit
[41:33] of the extra activity that would have
[41:34] come from having consumers that are more
[41:36] optimistic and so on. Okay?
[41:39] So this is actually this has happened a
[41:41] lot
[41:42] uh
[41:43] over the last few months.
[41:45] This is an environment people call it's
[41:47] an environment where good news is bad
[41:49] news.
[41:50] Okay?
[41:51] Good news about aggregate demand,
[41:52] consumers are happy, blah blah blah, is
[41:54] bad news or labor markets are very
[41:56] tight, wages are going up.
[41:58] All things that sound wonderful in other
[42:00] environments
[42:01] sound terrible news for the financial
[42:03] markets. Okay?
[42:06] For most, I mean there's difference in
[42:08] different sectors and so on, but but for
[42:10] the aggregate, for the average,
[42:12] it's bad news. So this is an environment
[42:14] where good news is bad news. Good news
[42:16] about aggregate demand, you have to be
[42:17] specific about what. Good news about
[42:19] aggregate demand is bad news
[42:21] for asset markets.
[42:23] It's not always like that.
[42:24] If you're in a recession,
[42:27] the Fed doesn't want to fight that. It
[42:28] wants to have more aggregate demand. So
[42:30] if you get good news about aggregate
[42:31] demand, that's very good news for asset
[42:33] prices
[42:34] because the Fed will not offset that and
[42:36] you get the positive effect of the extra
[42:38] dividends and things like that. Okay?
[42:41] So
[42:43] Okay.
[42:45] Another component that is that moves
[42:47] asset prices a lot. So monetary policy
[42:49] moves asset prices a lot. Okay? And and
[42:52] monetary but monetary policy doesn't
[42:54] happen in
[42:55] some separate isolated space. It it it
[42:58] reacts to news about the economy, about
[43:00] consumers, about firms, about regional
[43:03] banks, all sort of things. Okay?
[43:07] Uh another big driver of asset prices is
[43:11] this guy here
[43:13] of of equity in particular
[43:15] is this risk premium.
[43:17] Okay?
[43:18] So that risk premium can move a lot
[43:21] and and it's an important driver of
[43:23] asset prices.
[43:25] This index, this is the it's called VIX.
[43:28] VIX is I'm not going to explain what it
[43:30] is, but
[43:32] people call it so you get a the picture,
[43:34] an index of fear in an equity market. It
[43:37] it it's it's done
[43:38] Well, I'm not going to tell you what it
[43:39] is. It's it's based on option prices and
[43:42] so on.
[43:43] Uh so this is
[43:45] this is, you know, when people realize
[43:47] that COVID
[43:48] was coming and so what you see is that
[43:51] this thing exploded up.
[43:54] Big big risk off.
[43:56] That's a massive spike in the little
[43:58] excess.
[44:00] Well, not surprisingly look what
[44:01] happened to equity.
[44:03] You know, collapsed by 35% or so.
[44:06] Part of that was expected dividends,
[44:07] blah blah blah,
[44:09] but a lot of it was the risk off.
[44:11] And it's called risk off when
[44:14] markets are very fearful. They don't
[44:16] want to take risks, risk off. Okay? Uh
[44:20] the recovery actually also had a lot to
[44:22] do with
[44:24] the recovery on the risk environment.
[44:26] People were sort of
[44:27] getting used to the thing.
[44:29] But that recovery also was a result of
[44:31] very aggressive monetary policy. The Fed
[44:33] tried to offset this by it cutting
[44:35] interest rates very aggressively and
[44:38] that also gave a boost to asset prices.
[44:40] In fact, they did so much that we ended
[44:42] up with a big
[44:43] lots of overvaluation in asset prices
[44:46] and then that's the reason when they
[44:47] hiked rates, so we had big a big decline
[44:49] in asset prices
[44:50] as a result. Okay?
[44:54] What is this? Ah, look, this is
[44:57] you know
[44:58] over the weekend
[45:00] over the weekend the
[45:02] I I
[45:03] we talked about this in the previous
[45:04] lecture
[45:06] um essentially the First Republic Bank
[45:09] went under
[45:11] uh and JP Morgan absorbed it.
[45:14] Uh so people thought that um
[45:18] that on Monday was was good because you
[45:20] know, people thought that
[45:22] this mini crisis was over.
[45:26] Well, yesterday
[45:28] uh it turns out that that
[45:31] two other regional banks, their shares
[45:33] began to collapse in the same way as the
[45:36] First Republic Bank shares
[45:38] collapsed the week before. Okay? So
[45:41] panic immediately set in. So the VIX,
[45:43] the fear index
[45:45] This is intraday. So markets open here
[45:49] and and the shares of this this this two
[45:51] banks began to decline very rapidly
[45:54] and so
[45:56] VIX went up a lot.
[45:58] And what you do This is SP This is the
[46:00] main This is the SPX, the the main SP
[46:04] S&P 500. It's the main price index
[46:07] equity price index in the US
[46:09] immediately declined.
[46:11] Okay? So it's a That's the excess
[46:13] moving.
[46:14] Here excess move up
[46:16] little X
[46:18] and then it began to come down and the
[46:20] markets began to recover.
[46:21] So this risk on and off is a is a very
[46:25] big driver
[46:26] of equity prices.
[46:32] This is one of the banks actually
[46:34] that was in trouble.
[46:36] Uh
[46:37] You you see that
[46:39] but by the end of the day this this this
[46:42] this is
[46:44] PacWest. PacWest had the decline by 28%
[46:48] by the end of the day. But you see
[46:49] things look very weird here. They don't
[46:51] look like normal prices.
[46:53] Okay? Here they look like normal prices.
[46:55] They're moving all the time.
[46:57] Here they don't.
[46:59] What happens is that these prices
[47:00] decline so rapidly that they they
[47:02] trigger what is called circuit breakers.
[47:04] So the
[47:06] you cannot trade those those shares when
[47:08] they decline too rapidly. And that's
[47:09] done deliberately so this little X
[47:12] doesn't get completely out of control.
[47:14] People to calm down. Okay?
[47:17] And so it triggered several times.
[47:19] Just as
[47:21] the the whole idea is that people calm
[47:23] down.
[47:26] Is there a question? Yeah, there's some
[47:28] of us like
[47:29] The previous or this one? Yeah, the
[47:30] previous one.
[47:32] Is
[47:33] Are either of them dependent on the
[47:35] other or are they more just showing the
[47:37] same sort of trend? No, no. Okay, it it
[47:40] doesn't a good question. Uh uh
[47:43] This is the risk component only. So this
[47:46] is more independent what I'm saying.
[47:49] When this guy goes up, if nothing else
[47:50] happens,
[47:51] uh this will decline because you're
[47:53] discounting things more heavily.
[47:55] But it is true that there were some
[47:57] common elements. Like there there are
[47:58] also common elements, which is people
[48:00] got very worried about having another
[48:02] regional bank collapsing and so on. And
[48:04] so that that also created fear about the
[48:07] economy, which is an independent reason
[48:09] for this to decline. And normally in
[48:11] recessions as well, this risk in
[48:14] appetite is is is is lower. So so you're
[48:17] right that it's a common component. But
[48:19] the point I was highlighting is that
[48:21] is that this VIX sort of is a big
[48:23] driver. It has a big impact on asset
[48:26] prices.
[48:28] But it's not the cause.
[48:29] It was an event that caused both, but
[48:32] the fact that this event came with this
[48:34] biggest spike in in the VIX meant that
[48:37] that the impact on the equity index was
[48:39] was larger than if it had been only news
[48:41] about the economy, meaning that there
[48:43] was a recession ahead or something like
[48:45] that.
[48:46] And let me just finish with a with with
[48:48] the opposite phenomenon.
[48:51] You know,
[48:52] I was talking in episodes of fear, but
[48:54] sometimes markets get very carried away
[48:56] in the opposite direction. Okay? And
[48:58] here I'm showing you you know, examples.
[49:01] I put together this picture many years
[49:03] back and now Deutsche Bank keeps
[49:05] updating it, which is it shows you some
[49:08] some It seems that the world needs a
[49:10] bubble somewhere.
[49:11] And then here it shows you several sort
[49:13] of big asset valuations, you know, look
[49:16] 500%.
[49:18] This here is the Nikkei. I mean, it was
[49:20] enormous appreciation of the Nikkei.
[49:22] Here was Bitcoin. Then it collapsed.
[49:24] Okay? They always end up bad. When you
[49:26] never you see this big sort of a spiking
[49:28] up, they almost always end up quite
[49:31] poorly. Now, this is
[49:34] is much more likely that it happens in
[49:36] equity than in bonds. In bonds, it
[49:37] cannot happen because there is a
[49:38] terminal date,
[49:40] a terminal value. So, so what happens
[49:43] with these kind of things, people dream
[49:44] that the value go will go to infinity.
[49:47] No, and it could because the thing will
[49:48] last to infinity and and you know, the
[49:50] price could go to infinity. For a bond,
[49:51] that cannot happen because it has a
[49:52] terminal date and at that date they're
[49:54] going to pay you 100, so it can't
[49:55] happen.
[49:56] But for equity, people's imagination can
[49:59] run very wild. In fact, there is a
[50:01] famous bubble, the South Sea Bubble.
[50:04] It's a company in the UK.
[50:06] It is a famous for many reasons, but but
[50:08] one of them is that Isaac Newton got
[50:10] involved in in this one. And and you
[50:13] know,
[50:14] he got carried away. He he sold, he made
[50:16] a profit, you know, he sold the shares
[50:18] at 7,000. He profited 3,500 pounds,
[50:21] which must have been an enormous amount
[50:22] of money at the time.
[50:24] Prices kept going up,
[50:26] couldn't resist, went back in, ended up
[50:29] losing 20,000 pounds, which must have
[50:31] been a lot of money. So, he famously
[50:33] said, "I can calculate the motions of
[50:34] the heavenly bodies, but not the madness
[50:36] of people." It's all about expectations,
[50:38] okay?
[50:39] Let me stop here.