action

Actions: modeling,assessment, managementDidier Folus
The origin of the stock market is linked to the emergence of corporations in the seventeenth century. Securities markets are organized between the seventeenth and nineteenth centuries in England, the United States, France, gradually taking the form of exchanges with operating rules and authorities. The action is as representative of ownership of a partner, which it provides a variable income. Actions are ubiquitous in economic circuits and in particular the financing of the company (section 1). The extent and nature of the actions justify their analysis in terms of modeling, assessment and management. The generic definition of action as property rights covering several asset classes and modes of transmission and various trading (section 2). The study of the action as financial security is based on the modeling of the temporal evolution of the price (section 3) and the analysis of its value in the light of models of financial theory (section 4). This study is essential both for the exchange of shares for cash, as futures exchanges or futures conditional. Finally, modern finance has created tools and methods for managing equity portfolios (Section 5).1. Actions in the corporate financeThe activity of a business requires investment, involving themselves funding. This funding is external (choice of funding instrument: equity or debt), or internal (flow resulting from operating cash flow). The private equity, embodied by the issue of shares, materializes the role and rights of investors, shareholders of the birth of the company ~ I and during his life (Ginglinger, 1991). How actions are part of the external financing of the company is described in Figure 1.1. The choice of financial structure refers to the concept of leverage, the thesis of Modigliani and Miller (1958, 1963), as well as theories of agency and the signal (and Jacquillat Levasseur, 1984; Charreaux , 1987, Harris and Raviv, 1991).4.3. Models practitioners: discounted cash flow in some universeIn deterministic universe, an investor who places the sum S at time twishes to recover at time t + 1 capital equal to Si + i = S, (1 + rt + i), where rt + l is the interest rate for the period [t, t + 1), a rate that reflects the value of "sacrifice)> agreed, the sum S being saved instead of being consumed. The value of an action defined by the following future dividends Dt + l, z + Dr, .... D isequal to the sum of these flows discounted at rate required by the market at each reporting date:\DTT [23]11 ~ 1 + 'rs) \ 5 = r + i /The ability to assess an action depends on the ability of the assessor to correctly estimate the future cash flows and to choose a suitable discount rate for each period, which requires knowledge of the term structure of rates interest. In practice, this difficulty is outlineborn in replacement rates r, by their geometric mean 1'R, where the classical expression of the value of a share:The weight of dividend closest is paramount and a variation of the amount of dividends will close a greater influence on the value of the action that the same variation of dividends far. The estimate of future dividends is obtained from the financial analysis of the company using predictive methods based on the development of investment plans and financing flows associated tables.4.3.1. The model of Gordon and ShapiroThe most famous deterministic models for the shares is the "perpetual growth model -> Gordon and Shapiro (1956), the assumptions are as follows:- The firm generates a series of benefits B, I3, _ ~, I3,- The firm pays dividends shareholders Series D, 1), +, D,- The rate of earnings growth is g = he), where i. E [-l. 1] is the rate of return on investment of the firm and b E [0. 1] the retention of profits; g is the annual growth rate of the dividend. A portion of the profits are reinvested in the firm so that its growth is entirely self-financed (no debt) and, logically, g <i.At the time r> t, we have B = Bt (1 + g) and DT = T f (1 - b) I3T - D (1 + g) j; innoting the discount rate r, the theoretical price of the shares at the current time t is given by:Dt (l + y) Dt (l +. Y) * 2 _ ~. . . Dt + (l + g) _1 + r + (1 + "r) z (1 + r ~ xFor there is growth, it is necessary that z profitability of funds invested in the business is greater than the cost of capital r (see below), if this is not the case, the company is not profitable enough to satisfy r rate required by the market, thus r <i. In addition, g must be less than r for the value of the firm is not infinite. Thus, (1 + g) / (1 + r) <l, and therefore the range ofgeneral term [(1 + g) / (1 + r)) 'converge33 to (l + g) / (' rg) • Therefore,Equation [25] becomes:(1Sr + g) D + Dt + i [26]=• r - r q-gThis expression means that any time simply estimate the next dividend and have a discount rate r> - g for the value of the action. The action is even more expensive than the business is profitable (ii high) or distributes a significant portion of its earnings (g is high). However, ceteris paribus, a lower cost of equityr adds the share price.4.3.2. The use of the price earning ratio: Bates modelThe price earnings ratio (PER) is the ratio of share price to earnings per share (EPS): The PER indicates in years the minimum holding period33. When -1 <a <1, the series of general term (a) "converge: we show that[Z7 ~]- Dt + iDr + z+ + ...(1 + Tt + l) (1 + rt + t) (1 + r 2 c)T = i +1Sr =DTT t-1 (1 +, /.)[...]Title necessary to obtain reimbursement through BPAj4. A priori, a low PER indicates as cheap as EPS, dividend and therefore allows the holder of a security to be quickly repaid the investment. In contrast, a high PER indicates an action chère3i. This indicator is simple to calculate, is widely used in practice, but criticized by theorists of finance because it combines two values, one of which is accounting (BPA) and the other is a market price (price action), which make it diverse and deprive him of much of its meaning. Nevertheless, it is interesting to know how to use it in the evaluation of actions. The model of Bates (1962) used the PER to address the following problem: given the current PER of action and a projected growth rate of the BPA, at what price should you sell the stock after T years detention for a return r fixed in advance? The notations of the previous model are included, and:- The firm generates a series of BPAI earnings per share, EPS, 13PAr + i - d = 1 - b is the rate of distribution of profits,- BPAT profit is T> t, we BPAT Bout = (1 + q) Ttis the share price at the date 7 'which provides annual profitability • r.At the initial date, PER = SI / EPS and PER which provides annual profitability r after T years writing PER; 1 = ST / BPAT (1 + y) Tr ModelBates shows how to calculate the PER-ç, sales threshold "in explaining the price ST as the capitalization rate r of the original price on T - t years (equation [271) and as E T multiplied by the BPA in T ( Equation [281):ST = IF (1 + r) T-t = PERtI3PA, (1 + r) T `ST = PER1 BPA, BPA = 7-E (1 + g) ~ '-tThis equation gives the PER which the investor must sell his title to achieve annual return equal to r •. This expression considers that the company reserves the dividends for its activity. When dividends are paid to shareholders, return it gets r both in terms of gain on the action and the reinvestment of dividends at the same rate. Thus, the value expressed by the equation [27] should be reduced by the aggregate amount of dividends discounted at the rate r, which leads to:Equation [30] gives the minimum PER of purchase for returns r, taking into account the payment of dividends. Equation [30] generalizes the model34. BPA is equal to the net income of the company divided by the number of shares comprisingGordon and Shapiro, simply replace E by .5 "/ BPA and noted that D = dx BI'A. Failure of this model is to think in finite horizon for evaluating an action. Bates model provides results whose quality depends heavily on the proper estimation of its parameters, and in particular the knowledge of future profits. sake of realism, Bates and Molodovsky, May and Chottiner (1965) used a growth rate of profit rate Dividend and different discount rates for each period, and proposed a tabulation.4.3.3. Holt model and the payback periodInspired by Holt (1962), the payback period is the number of years required T * for the sum of future profits, discounted at the risk-free interest rf economy equals the share price. In the notations above, S is the sum of T * under a geometric progression I3PAt first term and reason (1 + g) / (1 + r f), where the expressionThis formulation assumes that all profits are distributed, it is less flexible than Balls. In addition, it limits the horizon taking into account the earnings stream, which contradicts the theoretical evaluation of actions. Finally, we can see the role of the rate of profit growth: two securities with the same RIP, which has the highest earnings growth will be highest within the shortest recovery and will be considered the cheaper. However, as the PER, the payback period appears to be an ad hoc indicator, this (limit himits scope.5. The implications of the model for managing a portfolio of stocksModels of finance theory have practical implications on the assessment and management of a portfolio of shares.5. 1. The discount rate and the cost of capital of a companyModel the evolution of the share price using a stochastic process returns to explain the process of updating. "For example, [0. T], equation [4] led to the updating process.; ~ CXH-r = {} if llt • B't III = Fi. in the stochastic case, equation [12] gives ~ -5't = BoutE rpi j[28]whenceZ * = t + hi I1-C ~ f - • ~ \+1- l. f /- L + gInl + rr[27 ~ _ [28] _> E * = E, + i,.l + g-R[29]C 1 + r • \ t I T-1 +9)l +. ~ i / ~ + (7 9(~PERT = RIP1 + r ~ T-t11 + g ~