Welcome back. Today, we are going to talk about a very specific form of insurance strategy which we call Constant Proportion Portfolio Insurance or CPPI in short. CPPI strategies are very commonly used and they are definitely worth looking at. The CPPI strategies have been introduced by Black and Jones in 1987. It is a procedure that allows you to generate convex option-like payoffs without using option. So it's all about dynamic allocation strategies between risky and safe assets that allow you to get downside protection and upside potential at the same time. Now, the principles behind CPPI strategies are actually very simple. What you're going to do is you're going to allocate to a risky asset in multiple M of the difference between your asset value and a given floor. So if you think about your wealth level or your asset level as being the current value of your assets and you think about a floor, which is the minimum level for your assets, that something that you don't want to go below, that's the minimum that you think is extremely important to protect. Now, the procedure tells you that if you look at the difference between your asset value and the minimum callback to cushion, well, that's how much you can put at risk because if you cushion decreases and at some point it go to zero, if you keep on taking risks at this age, you may go below the floor which by assumption is something that you want to avoid at all costs. What the strategy says is something very simple; at every point in time, you're going to take a look at your cushion, so asset value minus the flow, and you're going to allocate to the risky asset, a multiple of that cushion. So what happens clearly is if even when the cash goes down, you're reducing the risky asset allocation. Eventually, if you keep on losing ground as the cushion gets to zero, as your asset value gets to your floor, then your actual allocation is the multiple M times zero because now it go to zero cushion. So now, you're allocating nothing to risky assets 100 percent at this point in time of your assets allocated to your safe component of your portfolio and that allows you to protect your floor. Well, let's take a look at the specific example. Let's assume that the multiplier M is equal to 3, let's take a look at a floor which is 80 percent of your current wealth if you will. The question that you want to ask is at this point in time, if you have 100 percent of your wealth, your floor is at 80 percent, how much should you allocate the risky component in this CPPI type mechanism? Well, the answer is very simple. You look at $100, which is your initial wealth, you look at the floor, which is 80 percent of that, which is $80, so the distance between the two, the cushion is $20. So you're going to allocate the multiple M which is 3 times $20. So in this case, you are going to allocate $60 the performance seeking portfolio, the risky asset, and $40 will be invested in the safe asset. Again, if you're losing round, if margin for error disappears, then you are going to keep decreasing that allocation. Now, the beauty of the CPPI strategy is that if you implement it carefully and if you're willing to trade extremely often in the limit you're trading continuously, then nothing can go wrong. What's going to happen is as you get close to the floor, you're reducing the allocation and as you hit the floor, your allocation goes to zero. Now in implementation practice, you may not be able or willing to trade on a daily basis because that will generate lot of transaction costs. But what might happen is you may be trading on a monthly basis, on a quarterly basis. So if you're trading on a quarterly basis, it could happen that between two trading dates, the loss in the risky component is so large that then you get below the floor before having time to trade. In principle, you should trade continuously so when you hit the floor you should be at zero. But if you trade on a quarterly basis maybe you're now here and then the next quarter you slightly below the floor, well, it's too late when you trade, you're already below the floor. The risk of breaching the floor because of discrete trading in CPPI strategy is known as gap risk. Gap risk will materialize if you're not trading sufficiently frequently. You could actually show that gap risk will materialize if the loss on your risky portfolio compared to your safe component is higher than 1 over the multiple, 1 over M. Let me take an example. Let's say M is equal to 5, 1 over M is 1 divided by 5, it's 0.2. Well, that's 20 percent. Well, what you can show is that if within a quarter you're losing more than 20 percent in the risky portfolio relative to your floor, then you're going to breach the floor in this particular case. That's why it's recommended of course that you calibrate the multiplier as a function of the maximum potential loss within a given trading interval. Wrapping up. Constant portfolio proportion insurance strategies are pretty useful because they allow you to generate upside while providing you with downside protection. So it's a convex payoff just like the type of payoff you'd get with options except that you can implement it without option in this case. It's very convenient, typically works well except for these gap risk that you can manage by being very careful when calibrating the value of the multiplier. Next time, we are going to talk about some improvement or extensions if you will of the basic CPPI strategies and discuss several examples of application.