Financial Engineering

1. Carlos Gamez Math Finance Honor Society University of Utah Financial Engineering

2. What is Financial Engineering? • Financial Engineering refers to the bundling and unbundling of securities. This is done in order to maximize profits using different combinations of equity, futures, options, fixed income, swaps. • They apply theoretical finance and computer modeling skills to make pricing, hedging, trading and portfolio management decisions.

3. Financial Engineers are prepared for careers in:

4. Suggested Background Generally, Financial Engineers are strong on the following fields: • Statistics/Probability and PDEs • Stochastic Processes • C++ Programming • Basic Business Finance Theory

5. What is a security? • A security is a fungible, negotiable instrument representing financial value. • Securities are broadly categorized into debt and equity securities • such as bonds and • common stocks, • respectively.

6. What’s the purpose of securities? For the Issuer

7. What’s the purpose of securities? For the Holder

8. Equity and Debt Traditionally, securities are divided into debt securities and equity.

9. Debt Debt securities may be called debentures, bonds, notes or commercial paper depending on their maturity and certain other characteristics. The holder of a debt security is typically entitled to the payment of principal and interest, together with other contractual rights under the terms of the issue, such as the right to receive certain information. Debt securities are generally issued for a fixed term and redeemable by the issuer at the end of that term.

10. Equity • An equity security is a share in the capital stock of a company (typically common stock, although preferred equity is also a form of capital stock). • The holder of an equity is a shareholder, owning a share, or fractional part of the issuer. Unlike debt securities, which typically require regular payments (interest) to the holder, equity securities are not entitled to any payment. • Equity also enjoys the right to profits and capital gain.

11. Weighted average cost of capital The Weighted Average Cost of Capital (WACC) is used in finance to measure a firm's cost of capital.

12. Formula ∂ The cost of capital is then given as: Kc = (1-δ) Ke + δ Kd Where: Kc The weighted cost of capital for the firm δ The debt to capital ratio, D / (D + E) Ke The cost of equity Kd The after tax cost of debt D The market value of the firm's debt, including bank loans and leases E The market value of all equity (including warrants, options, and the equity portion of convertible securities) In writing: WACC = (1 - debt to capital ratio) * cost of equity + debt to capital ratio * cost of debt

13. The Modigliani-Miller Theorem The basic theorem states that, in the absence of taxes, bankruptcy costs, and asymmetric information, and in an efficient market, the value of a firm is unaffected by how that firm is financed. It does not matter if the firm's capital is raised by issuing stock or selling debt. It does not matter what the firm's dividend policy is. Therefore, the Modigliani-Miller theorem is also often called the capital structure irrelevance principle. ∑

14. Proposition y = C0 + D/E (C0 – b) * y is the required rate of return on equity, or cost of equity. * C0 is the cost of capital for an all equity firm. * b is the required rate of return on borrowings, or cost of debt. * D / E is the debt-to-equity ratio.