Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues

14

Market performance and risk measures

14.1 RETURN AND RISK MEASURES

14.1.1 Return measures

Returns relative to interest rate instruments and positions are straightforward, and have been treated in previous chapters regarding such interest rate instruments. This section is devoted to return measures for other instruments, mainly stocks. The extension to commodities products is straightforward, taking into account that in this case, there is no associated revenue like dividends for stocks.

Return on a Single Stock Position, and One Period of Time

During one period of time (i.e., 1 day, 1 month, 1 year or whatever), from t − 1 to t, let us denote S the spot price observed in the market of stock S, S being function of t. The rate of return, in short, the return rS “on the price” is

Besides, it may happen that during this single period of time, S is paying a dividend d: the return on the dividend rd, called dividend yield is

Hence, the total return:

Example. Compute the 1-year total return (10/21/10 to 10/20/11) on L'Oreal:

• 10/21/10 close price: €87.43;
• 10/20/11 close price: €78.47;
• net dividend paid: €1.80 (not taking account the dividend payment date).

Multi-periodic Return on ...