Welcome back. Today, we are going to talk about asset-liability management, and try and emphasize why and how the presence of liability matters when it comes to portfolio construction and portfolio decision. Let's start with this example on the brief discussion of the pension fund crisis. At the turn of the last millennium, there has been a major pension fund crisis. Well, let's take a look at the example of the US. Now, if you look at the collective defined benefit pension plans from the S&P 500 companies, so the largest companies in the US. From December 1999 to May 2003, those pension plans went from a net collective aggregated surplus of about $240 billion, and it eventually transform over the course of those few years into a net deficit of more than $250 billion. That's really scary. It sounds like $500 billion have just disappeared going from positive 250, to a negative $250 billions acquired. What exactly has happened? Well, there have been two primary explanation for this pension fund crisis. Something that people have called the pension perfect storm of adverse market conditions. Okay. On the one hand, what we've seen is the turn of the millennium, this is the burst of the tech bubble. The end of '99, the market, super expensive; tech stock, super expensive. Then going to 2000, 2001, 2002, 2003, the bubble explodes and then we see strong decreasing equity markets. That has translated into, of course, a sharp decrease in pension plan assets, at least the part of these assets that were invested in equity markets. Now, if it was only for the decrease in equity markets, the situation would have been bad. But actually the situation, as we saw, went from bad to ugly. Because at the same time, as asset value was going down because of decreasing equity markets. Liability values were going up because of decreasing interest rates, and given that the present value of the liabilities is essentially like bond portfolio, so the value of the liabilities go up. If the discount rate goes down, well, that's exactly what has happened. So it's a perfect storm of market conditions, asset value going up. As the value going down, liability value going up, then of course, the surplus becomes a deficit. Now, these are factual explanation, but something that we have to keep in mind is that what has happened is also signaling the weakness of risk management and asset allocation practices. I mean, after all, that's what risk management should be all about. Trying to immunize the situation, the welfare of pension funds and other asset owners with respect to changes in market conditions. Well, obviously something went wrong at that point in time. So that was at the turn of the millennium. Well, guess what? The same thing happened again in 2008, when we had the big collapse, of course, with the subprime crisis and then the consequences of the subprime crisis in terms of decreasing equity markets and other asset classes going down. Well, let us translate it again into a severely increasing concern for pension plans. This graph shows the situation in terms of funding ratio. In other words, assets divided by liabilities for different states in the United States, and here is where we find. We find that there is no state in the US in 2009 after this bare market situation that is at or above 100 percent. In other words, what that means is, in all of those states, the assets in place are not sufficient to cover the liabilities. In other words, there will be the need to turn to stakeholders and request additional contributions to meet those liability payments. As we can see there, a few states in which the deficit with actually very severe with the funding ratio which is less than 70 percent. Well, that's the situation in the US, by the way, similar situation in the rest of the world. Just a quick look at the situation in the UK. We are looking at the aggregate planning ratio of defined benefit pension plans in the UK. What we see is that, again, it's a deficit. We are looking at the surplus in terms of assets minus liabilities, and what we find is, this is almost always in the negative grounds. So what's the conclusion? Well, the conclusion is, when we manage assets against liabilities, what matters is not merely what happens on the asset side. What matters is what happens to the assets relative to the liabilities. In other words, if asset value goes down, but value goes down even more, this is not bad news. It's actually good news. So saying that I don't like when asset value goes down. Well, that's not a meaningful statements from an asset-liability management perspective. What matters is what happens to the funding ratio which, again, is the ratio of assets divided by liabilities. So if asset go down, but liability go down by more, then the funding ratio goes up as opposed to going down, right? Now, there's a related quantity that we've also been discussing which is the surplus. So the surplus is being defined as not the ratio of assets divided by liabilities, but assets minus liabilities. Of course, we call that the surplus when it's positive. We call that deficit when it is negative. Wrapping up, the bottom line is, what matters is not the value of the asset per se, having a sole focus on wealth is misleading. What do we have to worry is the value of assets relative to liabilities. So in particular, we have to focus on funding ratio, and funding ratio is an important indicator for telling us what's the fraction of the liabilities that you're able to cover given the existing assets. It is, if and only if, the funding ratio is 100 percent or above that you're in good shape because you're able to cover those liabilities. Next time, we're going to be introducing the concept of liability-hedging portfolios. We are going to argue that to achieve meaningful risk management practices, institutional investors, large asset owners, but also individuals, they need to equip themselves with these dedicated hedging portfolios.