The Basic Tools of Finance Copyright 2004

Finanace (財務金融) • Finance is the field that studies how people make decisions regarding the allocation of resources over time and the handling of risk. I. Value Comparison II. Risk Copyright © 2004 South-Western

I. Measuring the Time Value of Money (1) Receiving a given sum of money in the present is preferred to receiving the same sum in the future. (2) In order to compare values at different points in time, compare their present values. (3) Firms undertake investment projects if the present value of the project exceeds the cost. Copyright © 2004 South-Western

Present Value (PV，折現值) • Present value (折現值 or 現值): If r is the interest rate (assumed fixed), then an amount X to be received in N years has present value of: PV=X/(1 + r)N • PV refers to the amount of money today needed to produce a given future amount of money, using prevailing interest rates. PV*(1 + r)N =X Copyright © 2004 South-Western

PV • A sequence of future payments (Rt) produce a present value of •

FYI: Rule of 70 • According to the rule of 70, if some variable 70 grows at a rate of g percent per year, then that variable doubles in approximately 70/g years • eg, g=1 (growth rate=1%)， (1+0. 01)n =2 n*ln(1. 01)= ln(2) n= ln(2)/ ln(1. 01)= 69. 66年. = 70/1 • eg, g=3 (growth rate=3%)， (1+0. 03)n =2 n= ln(2)/ ln(1. 03)= 23. 45年. = 70/3=23. 33 • eg, g=8 n= 9. 01年. = 70/8 =8. 75 Copyright © 2004 South-Western

Asset Valuation • Fundamental analysis (基本面)： the study of a company’s accounting statements and future prospects to determine its value. • The value of an asset, eg, a share of stock, equals the present value of the stream of dividends and final sale price. Copyright © 2004 South-Western

Asset Valuation • To compare the price of stock (Ps) and its PV, stock is (1) fairly valued：Ps= PV (2) undervalued（低估）：Ps < PV (3) overvalued（高估）： Ps > PV • The goal is to buy undervalued stock. • Ps < PV → buy Copyright © 2004 South-Western

Efficient Markets Hypothesis • The efficient markets hypothesis：（效率市場假說） theory that asset prices reflect all publicly available information about the value of an asset. • A market is informationally efficient when it reflects all available information in a rational way. (1) impossible to have arbitrage (套利：賺差價) (2) the only thing to do is buy a diversified portfolio. Copyright © 2004 South-Western

CASE STUDY: Random Walks and Index Funds • Random walk （隨機漫步） the path of a variable whose changes are impossible to predict. • If markets are efficient, the stock prices follow a random walk. • All stocks are fairly valued and no stock is more likely to appreciate than another. • Index Funds Copyright © 2004 South-Western

II. Managing Risk • A person is risk averse (風險趨避) if she exhibits a dislike of uncertainty. Fig 27. 1: • Ways to reduce risk: 1. Buy insurance 2. Diversify 3. Accept a lower return on their investments Copyright © 2004 South-Western

Figure 27. 1 Risk Aversion Utility gain from winning $1, 000 Utility loss from

1. The Markets for Insurance （保險市場） • Because of diminishing marginal utility (concave-shaped utility function), most people are risk averse. • The general feature of insurance contracts is that a person facing a risk pays a fee to an insurance company, which in return agrees to accept all or part of the risk. Copyright © 2004 South-Western

2. Diversification of Idiosyncratic Risk • Diversification (風險分散) ： the reduction of risk achieved by replacing a single risk with a large number of smaller unrelated risks. • Idiosyncratic risk （專屬的風險）： the uncertainty associated with specific companies. Copyright © 2004 South-Western

Diversification of Idiosyncratic Risk • Aggregate risk （總體性的風險）: the uncertainty associated with the entire economy. • Diversification can remove idiosyncratic risk, but cannot remove aggregate risk. • Fig 27. 2: Copyright © 2004 South-Western

Figure 27. 2 Diversification Risk (std of portfolio return) (More risk) 49 Idiosyncratic risk 20 Aggregate risk (Less risk) 0 1 4 6 8 10 20 30 40 Number of Stocks in Portfolio Copyright© 2004 South-Western

3. The Trade-off between Risk and Returns • People can reduce risk by accepting a lower rate of return. • Normally, assets with higher risk are compensated with higher rate of returns --- Risk Premium (風險貼水) Fig 27. 3 eg, 2006/3 金管局考慮雙卡設利率上限： 10 -12%，是否合理？ Copyright © 2004 South-Western

Figure 27. 3 The Tradeoff between Risk and Return (percent per year) 8. 0 25% stocks 50% stocks 75% stocks 100% stocks No stocks 3. 0 0 5 10 15 20 Risk (standard deviation) Copyright© 2004 South-Western

Summary People receive the real return for saving to compensate the deferment of consumption. • Use PV to compare sums from different times. To make an investment： to Max current returns? to Max PV? • The value of a share of stock equals the PV of the stream of dividends and the final sale price. Copyright © 2004 South-Western

Summary • The efficient markets hypothesis：financial markets process available information rationally, so a stock price always equals the best estimate of the value of the underlying business. • However, irrational psychological factors also influence asset prices. • Risk-averse people can reduce risk using insurance, through diversification, and by choosing a portfolio with lower risk and lower returns. a balance between expected PV and risks Copyright © 2004 South-Western