[MUSIC] So welcome on this first lesson on defining risks, which will provide you with some insights into forward and option contract. And what are the learning objectives that we had? First of all, what is a forward, what is an option contract? Secondly, how do these contracts differ from primary assets, such as stocks and bonds? And what are the payoff structures at maturity? And, finally, how can we use forwards and options in portfolio management? So let me first introduce a derivatives contract or a derivatives instrument. It is a contract whose value depends on the price of the so-called underlying asset. And the underlying asset could be a stock, could be a bond, could be an exchange rate or an index or a natural resource. There's many underlying, or so-called primary, assets. And the derivative's price will evolve as the underlying price evolves. So we can talk about the forward contract written on an exchange rate, for instance, the euro, dollar exchange rate. Or we can talk about an option contract written on the Swiss Market Index, the so-called SMI index, just to take two examples. So when we talk about the markets, derivative markets are huge markets. We'll see it in a minute. And they can be traded either on standardized exchanges, such as the CBOE, which stands for Chicago Board of Options Exchange. Or they can be traded, as we call, OTC, which means Over-The-Counter. So what is the feature of these contracts, are they the same? Mostly, they are the same. But there's a huge difference in the sense that contracts, forwards or options that trade on regular exchanges are standardized to enhance the liquidity on these markets. Whereas, contracts that trade OTC, over-the-counter, will be tailor-made to the customer. However, one of the key differences will be that OTC markets are actually subject to the counterparty risk, which you don't have on exchange-traded contracts. And when we talk about how big is the size of the derivatives markets, we introduce a notion which is so-called the notional value of these instruments. And the notional value is simply the units of underlyings that you have in a given contract multiplied by the spot value of that underlying or primary asset. So just to give you an idea of the size, the size has grown exponentially over the time period under review. And you can see here the green bars reflect OTC contracts. The yellow bars reflect the exchange-traded derivatives. So one key issue, first, is that most contracts are OTC-traded and thus subject to counterparty risk. The second important point is to see that the volume actually peaked over $700,000 billion just before the subprime crisis in 2008. And from 2005 until 2015, we actually had an increase of about 83% in the notional value of derivatives traded. So these are large markets and we'll see later why they are so important for portfolio management. So let me now start by defining what a forward contract is. So a forward contract gives its owner, its beneficiary, a firm commitment to buy or sell an underlying, for instance, index or exchange rate, at a prespecified date, which we call the maturity date of the contract, and at a prespecified price which is the forward price of the contract. So I give you an example,. Mr. Smith buys on the 22nd of April a forward contract on 1 million euros against the dollars, and at the forward price of $1.655 per euro. And the contract expires the 30th of May. So what is the correct heuristic? If you look at this graph, this line, sorry, you will see that on the 22nd of April, Mr. Smith enters the contract, but there's no cash flow exchanges. The contract is initiated, but actually nothing takes place until the maturity date, the 30th of May, where Mr. Smith will have to pay $1,655,000, and get 1 million euros in exchange for that purpose by resettling his forward position. So here, we will now discuss the payoffs, that was the other objective. How does the profit and loss at maturity look from entering first in a long Swiss market in this contract. And what you have on the horizontal axis of this graph is the value of the SMI at maturity. And we enter that contract at a spot price of the SMI of 7,650 Swiss francs, when the forward price was quoting at 7,546, and the contract started the 6th of April 2016, and actually expired a little bit more than two months later. So what we see is that at maturity, for any given price of the SMI, at the maturity date of the forward, which is above the forward price that is the 7,546, he will make a gain. Actually, he can make an unlimited gain if the price of the SMI tends to infinity. Whereas, if the price at maturity of the SMI is below the forward price, he will make a loss. So Mr. Smith, if he enters this contract, will have a linear increasing payoff, which increases as the value of the SMI increases at maturity. Okay, so now we will look at, let's see, Mr. Clark, who has exactly the opposite position. He has sold the forward position on the SMI. So it means this contract has the same specification you entered the 6th of April, the maturity date is the 17th of June. The forward price at the time of the initiation was 7,546. And we see that if the SMI is below 7,546, he will make a gain, although this gain in now limited when the price of the SMI tends to zero. Whereas, if the price of the SMI is above the forward price, he could potentially make an unlimited loss. So let me, to finish, give you a quiz. So why do we need forwards and, for instance, a forward on the SMI? So suppose the situation of Mr. Clark, who owns a portfolio, who replicates the Swiss Market Index. And he owns this portfolio, and at the 6th of April he's very worried that over the next two and a half months maybe the value of the SMI will decline and, thus, he may lose on his portfolio. So what can he do to protect himself against a drop in the SMI? Well, you can go home and do the exercise, but I'll give you the answer here. What he can do is actually combine his long position, which is the yellow line that is straight up, with a short position in the forward written on the Swiss Market Index, and such in a way that he realizes a perfect hedge. What is a perfect hedge? It's the light green line on the profit and loss which just is horizontal at the zero level. It means that whether the SMI goes up or down at maturity, he will be totally break even. No gains, no losses. For instance, if the SMI declines in value, his portfolio value will decline, but he will gain, as we saw before, on the short position in the SMI. So forwards allow you to protect yourself fully, for instance, in this case against a drop in the Swiss Market Index. And that's very valuable if you want a very well-diversified portfolio. So thank you very much for this first introductory lesson into forwards. I think the key concept is that forwards allow you to hedge, protect the value of your portfolio gains to drop in an underlying asset's value. And the second key point was the linear payoffs that you have as a long or short owner of the SMI forward contract. [MUSIC]
