## Financial Modelling

Written by admin on May 21st, 2011however, the cost of issuing new debt will be greater than the cost of issuing new equity. This is because adding debt increases the default risk – and thus the interest rate that the company must pay in order to borrow money. By utilizing too much debt in its capital structure, this increased default risk can also drive up the costs for other sources (such as retained earnings and preferred stock) as well. Management must identify the “optimal mix” of financing – the capital structure where the cost of capital is minimized so that the firms value can be maximized.

MODIGLIANI-MILLER THEOREM

If there were no tax advantages for issuing debt, and equity could be freely issued, Miller and Modigliani showed that the value of a leveraged firm and the value of an unleveraged firm should be the same.

**INTEREST**

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Interest is a fee paid on borrowed capital. Assets lent include money, shares, consumer goods through hire purchase, major assets such as aircraft, and even entire factories in finance lease arrangements. The interest is calculated upon the value of the assets in the same manner as upon money. Interest can be thought of as “rent on money”.

The fee is compensation to the lender for foregoing other useful investments that could have been made with the loaned money. Instead of the lender using the assets directly, they are advanced to the borrower. The borrower then enjoys the benefit of using the assets ahead of the effort required to obtain them, while the lender enjoys the benefit of the fee paid by the borrower for the privilege. The amount lent, or the value of the assets lent, is called the principal. This principal value is held by the borrower on credit. Interest is therefore the price of credit, not the price of money as it is commonly – and mistakenly – believed to be. The percentage of the principal that is paid as a fee (the interest), over a certain period of time, is called the interest rate.

Interest rates and credit risk

It is increasingly recognized that the business cycle, interest rates and credit risk are tightly interrelated. The Jarrow-Turnbull model was the first model of credit risk which explicitly had random interest rates at its core. Lando (2004), Darrell Duffie and Singleton (2003), and van Deventer and Imai (2003) discuss interest rates when the issuer of the interest-bearing instrument can default.

Money and inflation

Loans, bonds, and shares have some of the characteristics of money and are included in the broad money supply.

By setting i*n, the government institution can affect the markets to alter the total of loans, bonds and shares issued. Generally speaking, a higher real interest rate reduces the broad money supply.

Open market operations in the United States

The Federal Reserve (often referred to as ‘The Fed’) implements monetary policy largely by targeting the federal funds rate. This is the rate that banks charge each other for overnight loans of federal funds. Federal funds are the reserves held by banks at the Fed.

Open market operations are one tool within monetary policy implemented by the Federal Reserve to steer short-term interest rates. Using the power to buy and sell treasury securities, the Open Market Desk at the Federal Reserve Bank of New York can supply the market with dollars by purchasing T-notes, hence increasing the nation’s money supply. By increasing the money supply or Aggregate Supply of Funding (ASF), interest rates will fall due to the excess of dollars banks will end up with in their reserves. Excess reserves may be lent in the Fed funds market to other banks, thus driving down rates.

Credit spread options: credit call spread is a “bearish” call spread, which has more premium on the short call. A credit put spread is a “bullish” put spread and has more premium on the short put.

Credit spread (bond): In finance, a credit spread is the difference in yield between different securities due to different credit quality. The credit spread reflects the additional net yield an investor can earn from a security with more credit risk relative to one with less credit risk. The credit spread of a particular security is often quoted in relation to the yield on a credit risk-free benchmark security or reference rate.

**RISK MODELING**

Risk modeling refers to the use of formal econometric techniques to determine the aggregate risk in a financial portfolio. Risk modeling is one of many subtasks within the broader area of financial modeling.

Risk modeling uses a variety of techniques including market risk, Value-at-Risk (VaR), Historical Simulation (HS), or Extreme Value Theory (EVT) in order to analyze a portfolio and make forecasts of the likely losses that would be incurred for a variety of risks. Such risks are typically grouped into credit risk, liquidity risk, interest rate risk, and operational risk categories.

Many large financial intermediary firms use risk modeling to help portfolio managers assess the amount of capital reserves to maintain, and to help guide their purchases and sales of various classes of financial assets.

Formal risk modeling is required under the Basel II proposal for all the major international banking institutions by the various national depository institution regulators.

Quantitative risk analysis and modeling have become important in the light of corporate scandals in the past few years (most notably, Enron), Basel II, the revised FAS 123R and the Sarbanes-Oxley Act. In the past, risk analysis was done qualitatively but now with the advent of powerful computing software, quantitative risk analysis can be done quickly and effortlessly.

**PORTFOLIO PROBLEMS**

In finance, a portfolio is an appropriate mix of or collection of investments held by an institution or a private individual. In building up an investment portfolio a financial institution will typically conduct its own investment analysis, whilst a private individual may make use of the services of a financial advisor or a financial institution which offers portfolio management services. Holding a portfolio is part of an investment and risk-limiting strategy called diversification. By owning several assets, certain types of risk (in particular specific risk) can be reduced. The assets in the portfolio could include stocks, bonds, options, warrants, gold certificates, real estate, futures contracts, production facilities, or any other item that is expected to retain its value.

Portfolio management involves deciding what assets to include in the portfolio, given the goals of the portfolio owner and changing economic conditions. Selection involves deciding what assets to purchase, how many to purchase, when to purchase them, and what assets to divest. These decisions always involve some sort of performance measurement, most typically expected return on the portfolio, and the risk associated with this return (i.e. the standard deviation of the return). Typically the expected return from portfolios of different asset bundles are compared.

Porfolio formation

Many strategies have been developed to form a portfolio.

Ø equally-weighted portfolio

Ø capitalization-weighted portfolio

Ø price-weighted portfolio

Ø optimal portfolio (for which the Sharpe ratio is highest)

VALUATION OF OPTIONS

Black–Scholes:

The term Black–Scholes refers to three closely related concepts:

Ø The Black–Scholes model is a mathematical model of the market for an equity, in which the equity’s price is a stochastic process.

Ø The Black–Scholes PDE is a partial differential equation which (in the model) must be satisfied by the price of a derivative on the equity.

Ø The Black–Scholes formula is the result obtained by solving the Black-Scholes PDE for European put and call options.

Binomial options pricing model: In finance, the binomial options pricing model (BOPM) provides a generalisable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein (1979). Essentially, the model uses a “discrete-time” model of the varying price over time of the underlying financial instrument. Option valuation is then computed via application of the risk neutrality assumption over the life of the option, as the price of the underlying instrument evolves.

Monte Carlo option model: In mathematical finance, a Monte Carlo option model uses Monte Carlo methods to calculate the value of an option with multiple sources of uncertainty or with complicated features.

REAL OPTIONS ANALYSIS

In corporate finance, real options analysis or ROA applies put option and call option valuation techniques to capital budgeting decisions.[1]

A real option is the right, but not the obligation, to undertake some business decision, typically the option to make a capital investment. For example, the opportunity to invest in the expansion of a firm’s factory is a real option. In contrast to financial options, a real option is not often tradeable—e.g. the factory owner cannot sell the right to extend his factory to another party, only he can make this decision; however, some real options can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the future. Some real options are

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