Chapter 9 The Basic Tools of Finance
Chapter 9 The Basic Tools of Finance Econ 202 - 01
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Date Created: 04/09/16
Chapter 9 ~ The Basic Tools of Finance Present Value: Measuring the Time Value of Money Section Prelude: Because savings can earn interest, a sum of money today is more valuable than the same sum of money in the future due to its lost purchasing power. A person can compare sums from different times using the concept of present value. The present value of any future sum is the amount that would be needed today, given prevailing interest rates, to produce that future sum. The financial system coordinates the economy’s saving and investment, which in turn are crucial determinates of economic growth. Participants in the financial system make decisions regarding the allocation of resources over time and the handling of risk. Finance is the field that studies how people make decisions regarding the allocation of resources over time and the handling of risk. Money today is more valuable than the same amount of money in the future: $100 dollar today can be collected and saved with interest; whereas, collecting that $100 dollars in the future misses out because of no interest earned in a bank, inflation and its subsequent loss of future purchasing power. Future Value is the amount of money in the future that an amount of money today will yield, given prevailing interest rates: ???? Future Value = (Present Value of amount of X) × (1 + ????) Compounding is the accumulation of a sum of money in; say, a bank account, where the interest earned remains in the account to earn additional interest in the future. Present Value is the amount of money today that would be needed, using prevailing interest rates, to produce a given future amount of money: It’s the amount you would have to deposit in a bank today in order to yield a future value in “N” years. Present Value = (Future Value of amount of X) ÷ (1 + ????)???? Discounting is the process of finding the present value of a future sum of money, because the possibility of earning interest reduces the present value below the amount X to be invested or saved: ???? PV (Present Value) = (FV amount of X) ÷ (1 + ????) The higher the interest rate, the more you can earn by depositing your money in a bank Interest rates determine corporate decisions whether to invest or save o This is why the demand for loanable funds decrease when interest rates increase When PV (benefit) > current cost of X; “borrow for investment” When PV (benefit) < current cost of X; “don’t borrow for investment, and keep (save) your money for later opportunities and/or run for the hills” Current cost of 6-acre farm is $70,000. In 5 years farm is $100,000. ???? 1 0.05 (5%). ???? =20.10 (10%). 5 5 1.05 1 1.276 & ???????? =1100,000 ÷ 1.276 = 78,370 and 1.10 = 1.211 & ???????? = 100,200 ÷ 1.611 = 62,073 ???????? 1 $70,000 (benefit > current cost ~ buy) & ???????? <2$70,000 (benefit < current cost ~ don’t buy) Rule of 70 70 If a variable grows at a rate of “X” percent per year, that variable will double in about years. ???? ???????????????????????????? r = 5% then 70/5 = 14 years and/or r = 10% then 70/10 = 7 years Just For Fun ???? Using a logarithmic equation to solve for number of years to double one’s money: 2 = (1 + ????) then 2 = (1 + 0.15) then 2 = (1.15) ???? then log 2 = N × log (1.15) then N = ???????????????? Then N = 0.3010= 5 years. ????????????????.???????? 0.0607 ???? 1/???? Another way to calculate the number of years to double your money: (1 + r) = √2 then (1 + r) = 2 1 1 log (1+????) ???????????????? then log (1 + r) ???? × log 2 then ???? = log2 which inverts to >>> N = ???????????? (????+????)then BINGO….. Managing Risk Section Prelude: Because of diminishing marginal utility, most people are risk averse. Risk-averse people can reduce risk by buying insurance, diversifying their holdings, and choosing a portfolio with lower risk and lower return. Risk Aversion is a dislike of uncertainty: People dislike bad things more than they like comparable good things. Pain of loss is greater than joy of winning. Based upon marginal utility. Utility (util) is a person’s subjective measure of well-being or satisfaction. The Utility Function shows how utility (utils), a subjective measure of satisfaction, depends on wealth. As wealth rises, the utility function becomes flatter, reflecting the property of diminishing marginal utility. The more wealth a person has, the less extra utility he or she would get from an extra dollar. The level of risk aversion is dependent upon marginal utility of personality types: People who are risk averse: have decreasing marginal utility – curve flattens out as one moves towards the right and up when wealth increases along the graph People who are risk seekers: utility increases at an increasing rate – upward steeping curve People who are risk neutral: utility is linear and increases at a constant rate Markets for Insurance is not to eliminate the risks inherent in life but to spread their costs around more efficiently. Insurance companies face two (2) problems because they can’t fully guard themselves against these problems, so they charge higher prices. As a result, low-risk people forgo insurance and lose the benefits of risk-pooling: Adverse Selection ~ a high-risk person is more likely to apply for insurance than a low-risk person, because a high-risk person would benefit more from the insurance protection. People with chronic health problems Someone who smokes cigarettes in bed Someone who is a reckless driver and texts or eats while driving Moral Hazards ~ when a consumer buys insurance, they are more likely to engage in risky behavior afterwards because of less incentives to play-it-safe or avoid risky behaviors. Being more careless with or not securing “possessions, valuables, things” after getting insurance Driving faster and more carelessly after getting insurance A person takes poorer care of himself after getting insurance Annuities ~ for paying a fee today to the insurance company, people receive regular incomes (payments) every year until they die for purchasing that policy. Diversification reduces risk by placing a large number of small bets, rather than a small number of large bets. A diversified portfolio contains assets whose returns are not strongly industry or sector related, and some assets will realize high returns and other assets will have low returns. The high and low returns average out, so the portfolio is likely to earn an intermediate return more consistently than any of the assets combined. Diversification is the reduction of risk achieved by replacing a single large risk with a greater number of smaller or smaller-sized and unrelated risks. Standard Deviation ~ measures the volatility of a variable ~ how much a variable is likely to fluctuate. A higher standard deviation indicates a higher volatility of an investment portfolio. Diversification can reduce firm-specific risk. Diversification can NOT reduce or eliminate market risk (such as, an economic recession). The Trade-Off between Risk and Returns & Standard Deviation (STD) Standard Deviation ~ is a statistic that measures a variable’s volatility and how much it fluctuates. The higher the standard deviation of the asset’s return; the greater the inherent risk. A low STD occurs when the data points tend to be close to the mean A high STD occurs when the data points are spread out over a large range of values As a rule-of-thumb: Ø Stock ~ STD = 0, 25% stock ~ STD = 5, 50% stock ~ STD = 10, 75% stock ~ STD = 15 & 100% stock ~ STD = 20 o Roger’s Rule-of-5 STD’s: (factor-of-5 ~ 0%/0, 25%/5, 50%/10, 75%/15 & 100%/20) Normal random variables stay within 2X standard deviations 95% of the time: o A portfolio of 100% stocks would have a risk of 20 STD’s +/- 2X STD’s. It would then have a range of 20 × 2 STD’s = 40 STD points. If the portfolio’s average returns are 8%, it would then theoretically have a “%” range of values from 8 + 40 = 48% in gains to 8 – 40 = -32% in losses. Firm-Specific Risk ~ is risk that affects and is related to only a single company. By increasing the diversification and the number of different stocks (assets) in a portfolio, reduces firm-specific risk. Market Risk ~ is risk that affects all companies in the stock market as when mostly all stocks decline as in either a recession or when negative “news” creates “fear” in the overall markets. The trade-off that is most relevant for understanding financial decisions is the trade-off between risk and return. Allocating more stock in a portfolio increases returns and thusly the risks. Conclusion: The two (2) important building-blocks of finance are time and risk….. Asset Valuation & the Valuing of Stock Section Prelude: The value of an asset equals the present value of the cash flows the owner will receive. For a share of stock, these cash flows include the stream of dividends and the final sale price. According to 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. Some economists question the efficient markets hypothesis; however, and believe that the irrational psychological factors also influence asset prices. Supply and demand determine the price of a stock. Fundamental Analysis ~ is the study of a company’s accounting statements and future prospects to determine that company’s value and ability to earn profits. A company’s value is determined by: (1) the amount its product or service is demanded, (2) its competition, (3) its present capital, (4) its labor force and unions, (5) its customer loyalty, (6) taxes, (7) government regulations and (8) etc. Valuing a Share of Stock: Stock’s Value = Present Value of Dividends + Its Present Value Selling Price Example: Future stock price of AT&T in 3 years could be $30 dollars paying $1 dollar dividend yearly… 1 1 1 30 1.10 + 1.10 + 1.10 + 1.103= 0.91 + 0.83 + 0.75 + 22.54 = $ 25.03 (compare this value to the stock price) Overvalued ~ If today’s share price is > than the stock’s calculated value Undervalued ~ If today’s share price is < than the stock’s calculated value Fairly Valued ~ if the price of a company’s stock equals its value Dividends ~ are the cash returns given to shareholders when a company is profitable Uncertainties & Shortcomings to Valuing Stocks You don’t know for sure what the stock price will be in 3 years You don’t know for sure if the interest rate will change over the years You don’t know for sure if the dividend will increase, decrease or remain the same 3 Types or ways to approach Fundamental Analysis Do your own research by reading annual reports of companies Rely on Wall Street analysists Buy a mutual fund in which its manager conducts fundamental analysis in its portfolio A Prospectus ~ is a document that provides fundamental information about a company’s valuations and shares before they are offered to be sold. “Past performance is no guarantee of future results.” Efficient Markets Hypothesis (EMH) ~ is the theory that asset prices (allegedly) reflect all publicly available information about the value of an asset and reflects the company’s future profitability. Each company listed on a stock market exchange is closely followed by many money managers The market price is set by the equilibrium of supply and demand ~ balance between buyers and sellers at any given price o This reflects the fact that this is a zero-sum game of winners and losers o The final price of the day is the final agreed upon price or settled price Informational Efficiency ~ is the description of asset prices that rationally reflect market prices from all available information and how those stock prices change when information changes. Best evidence supporting the efficient markets hypothesis is the use of index funds which is a complete basket of all the stocks in an index; such as, Dow Jones Industrials, S&P 500 and the NASDAQ Composite and 100 Indices. Index funds tend to beat managed mutual funds. The Efficient Markets Hypothesis states that it’s generally impossible to “beat the market.” 3 Main Implications of the EMH (Efficient Market Hypothesis): 1. Each stock price (allegedly) reflects all available information about the value of the company. 2. A stock price only changes in response to new information “news” about a company’s value. News cannot be predicted; so stock price movements should be impossible to predict. 3. It is impossible to systematically beat the market. By the time the “news” reaches you, mutual fund managers have already acted on it. Random Walk Theory ~ means that changes in stock prices are impossible to predict from the available public information. According to the random walk theory, the only thing which can move stock prices is “news” that changes public perception of a company’s value. And “news” in itself is unpredictable. Changes in stock prices are impossible to predict from public information. Index Funds versus Managed Mutual Funds An index fund or exchange traded fund (ETF) is a type of mutual fund that buys (allocates) all of the same stocks that are in a given stock index; such as, the Dow Jones Industrial Average, the S&P 500 Index or the NASDAQ composite or NASDAQ 100. Actively managed mutual funds buy and sell the “best” stocks and competes against other mutual fund managers and their mutual funds Actively managed mutual funds have higher expenses than index funds due to frequent trading From the EMH theory, returns of actively managed funds “usually” have lower returns over- time as compared to index funds. Index funds have lower fees and expenses as a result of less trading in-and-out within its basket of stocks. Speculative Bubble ~ occurs whenever the price of an asset rises (extremely fast) above what appears to be its fundamental value in an unusually short period of time due to speculative buying. An exhaustion gap (and reversal) occurs when the last buyer (speculator) is left holding (bought) the “bag” after a quick and large run-up: Then the profit-takers and short-sellers move in for their coup-de-grace and sell-off the market in order to collect their gains. John Maynard Keynes referred to these irrational waves of optimism and pessimism as being possessed by “animal spirits.” “Extraordinary Popular Delusions and the Madness of Crowds” ~ the book by Charles Mackay Stock market fluctuations often go hand-in-hand with fluctuations in the economy more broadly. CHAPTER 9 REVIEW & SUMMARY OF QUICK NOTES If during the year the interest rate rises, this decreases the present value of your future payment. Individuals who are risk averse are more negatively affected by bad events than they are positively affected by good events with the same dollar value. Therefore, if you are offered a bet with 50% probability that you would gain $1,000 and 50% probability that you would lose $1,000, you would not be willing to accept it since the loss in utility from losing the bet is larger than the gain from winning. In other words, if your level of wealth is currently at point B, then the gain in utility when going from point B to point C is much less than the lost utility by going back from point B to point A. The law of diminishing marginal utility states that the consumption of the first unit of a good or service gives you more satisfaction than does the second or third unit. The implication of this property of the utility function is that marginal utility decreases as you have more units of something. The graph shows that the risk of a portfolio falls as the number of different stocks in the portfolio increases. This suggests that placing your wealth in a variety of different stocks is a less risky strategy than tying your wealth to the fortunes of only a few firms. You cannot, however, eliminate all risk associated with a stock portfolio. Diversification is the practice of reducing risk by avoiding a substantial individual risk in favor of a large number of smaller, unrelated risks. Diversification can remove firm-specific risk from a portfolio, but it cannot eliminate market risk. Firm-specific risk is the risk associated with a specific company. Market risk is the risk associated with the entire economy, the performance of which impacts all companies traded on the stock market. Graphically, the persistence of market risk is illustrated by the fact that increasing the number of stocks in a portfolio leads to smaller and smaller reductions in risk as the standard deviation of the portfolio's return approaches 20%. The standard deviation measures the volatility of a variable—that is, how much the typical observation deviates from that variable's average. For a portfolio's return, the standard deviation measures how much the return typically varies from the portfolio's average return. As the graph illustrates, the standard deviation of a return for a portfolio with fewer stocks tends to be higher than that of a portfolio with many different stocks. For example, the return on a portfolio with four different stocks has a standard deviation of 32%, while the return on a portfolio with 20 different stocks has a standard deviation of 21.5%. The return on the portfolio with 20 different stocks will be less volatile than the return on the portfolio with only four stocks. Diversification is the reduction of risk achieved by replacing one risk with a larger number of smaller, unrelated risks. As we saw, it's impossible to eliminate market risk. To some extent, the performance of all companies traded in the stock market depends on the overall performance of the economy. Reductions in firm-specific risk will be largest when an investor chooses a portfolio with stocks from different, relatively unrelated sectors of the economy. Among the companies listed in the table, the most diversified portfolio would consist of stocks from different industries, whereas the least diversified portfolio would consist of stocks from the same industry. Note from the table that a portfolio consisting entirely of government bonds with no stocks (combination A) offers Yvette an average annual return of 2.5% and zero risk. At the opposite extreme, a portfolio consisting entirely of stocks (combination E) offers a substantially higher average annual return of 6.5% but comes with considerable risk. Specifically, the return on the all-stock portfolio has a standard deviation of 20%, compared to 0% for the all-government-bond portfolio. Recall that the standard deviation of a portfolio's return is an indicator of its volatility. Higher standard deviations are associated with more volatile returns. The standard deviation of the return for a portfolio consisting of 50% stocks and 50% bonds is 10%. The average annual return for the same portfolio is 4.5%. The returns for this portfolio will typically stay within two standard deviations, or 20%, of the average annual return. The returns will typically vary from a gain of 24.5% (two standard deviations above the mean) to a loss of -15.5% (two standard deviations below the mean). The efficient market hypothesis states that markets quickly integrate all available information so that the price of a stock or other asset reflects all available information. According to the hypothesis, all stocks are fairly valued at all times. Market price is determined by equilibrium between demand and supply. At the market price, the number of people who think the stock is overvalued (sellers) exactly equals the number of people who think it is undervalued (buyers). This supports the notion that the stock market is informationally efficient. Proponents of this hypothesis believe that buyers are rational, so prices are based on the underlying value of a stock. The market continually adjusts to new information; therefore, prices follow a so-called random walk, or a path that is impossible to predict. Because markets continually adjust to new information, proponents of the efficient market hypothesis do not believe that investors can accurately predict changes in stock prices; they believe the best an investor can do is purchase a diversified portfolio. A speculative bubble occurs when asset prices rise above what appears to be their fundamental value. This can happen if people are willing to pay more than the fundamental value for an asset on the premise that another person will buy the asset for an even higher price in the near future.
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