(A.1) Histograms and the 2008 Financial Crisis
Histograms caused the Great Recession—bad histograms, that is. In 2008 major investment banks started failing. It seemed none of the big banks would exist in a year if they were not bailed-out by the government. For years they had all made bad bets in the housing market, took on too much risk, and borrowed too much money. These were bad bets partly because they were made based on erroneous histograms. Investors made irrational financial decisions which brought down the whole economy and resulted in the largest recession since the Great Depression, so don't tell me histograms are not important!
The FCIC concluded that the rating agencies were as culpable as other financial institutions in causing the Crisis, stating, “The failures of credit rating agencies were essential cogs in the wheel of financial destruction. . . . Investors relied on them, often blindly.” The “forces at work” behind flawed ratings included “flawed computer models
[histograms]...
...
Moody’s, the commission’s case study in this area, “relied on flawed and outdated models
[histograms] to issue erroneous ratings on mortgage-related securities, failed to perform meaningful due diligence . . . and continued to rely on those models
[histograms]
even after it became obvious that the models were wrong...
—Edward Conard explaining the causes of the 2008 financial crisis in his
2012 book Unintended Consequences. Portfolio/Penguin Publishers: NY,NY.
[Note that many of the "computer models" were simply histograms].
(A.2) Histograms and Value-at-Risk (VaR)
Histograms played such a large role in the 2008 Financial Crisis because they were the major tool used in risk management. Some firms voluntarily adopted the use of histograms, but government regulations made others adopt it also. To measure how much risk a firm is taking there must be a measurement of risk, and almost all financial firms used (and continue to use) Value-at-Risk (VaR), which is essentially one segment of a histogram. Regulations dictate to firms how much collateral they must hold at any given time, and this level of collateral is directly determined by a firms' VaR value.
VaR and their associated histograms were such big players in the crisis an entire book was written about it.
Figure 1—A Book About VaR and the 2008 Financial Crisis
Watch this three-minute clip from the movie Margin Call, about how a Wall Street firm might have survived the 2008 Financial Crisis if they had discovered their financial problems before the meltdown began. Note they explicitly refer to VaR, and the importance the fictitious company places on VaR.
Video 1—VAR in the Movies
(scene from Margin Call (2011))
(For browsers other than Internet Explorer)
If you have trouble seeing the video click here.
Anyone who has taken a college-level statistics course can understand VaR. It works as follows. First, the firm has its analysts construct a histogram showing the probability of earning profits within a given interval—like, "What's the probability we may lose between 0.5 and 0.99 million dollars?" Using computer and statistical models, it describes the probability of profits and losses of a certain value in a bar chart. This probability may refer to profits the following day, month, quarter, or the following year. An example is given below in Figure 2.
This histogram shows the firm will probably make money, but it stands a 45% chance of losing money and a 5% change of losing one million dollars or more. To determine the firm's VaR it simply reads off the histogram. The firm selects some probability threshold, usually 5%. Regulators often choose this threshold for the firm. After choosing the threshold, the firm then observes the simulated losses at that threshold. At a threshold of 5% the firm loses $1,000,000 or more, and that is the VaR. It can also be interpreted as the threshold of profits/losses for which the sum of the left bars equals the VaR threshold (here, 5%), and the sum of the right bars equals 100% minus the threshold. In Figure 2, at losses of one million dollars there is only one histogram bar at that number and to the left, and its height is 5%, so the VaR is ($1,000,000)—note, the (.) is an accounting indicatation that whatever is inside the brackets represents losses or expenses, money going out. The sum of the bars to the right is 95%, or 100%-5%, so again, the VaR is ($1,000,000). The VaR is precisely one million dollars. That's all VaR is. A modern financial firm may need lots of computers, number-crunching, and "quant jocks" to get the histogram, but once the histogram is constructed getting the VaR is easy.
Figure 2—Histograms and Value-at-Risk (VaR)
Now that we understand what VaR is, how did it bring down the economy? Financial firms simply did not construct good histograms. They paid too much attention to the fancy math but not enough attention on quality data. The probabilities on the y-axis were not correct. Consider AIG, a firm that made money by insuring home loans. A bank that just sold a lot of home mortgages (i.e., loaned lots of people money to buy houses) might buy insurance from AIG to protect themselves in the event that the borrower doesn't repay. Use the analogy of car insurance.You pay the insurance company regardless of whether you get into a wreck. If you do not get into a wreck the insurance company makes money on your policy, but if you do wreck they lose money on your policy. Likewise, AIG made money when borrowers did not default on their home mortgages, but had to pay large indemnities if borrowers did default.
To manage its risk AIG would forecast the default rates on the mortgages it insured and construct a histogram of next quarter's potential losses and profits. Let's pretend Figure 2 was the histogram for AIG and its VaR was one million dollars. Perhaps AIG would keep one million dollars in cash or liquid assets to offset its risk. This one million dollars represents the "collateral" firms want to hold—and are required by regulations to hold— in case their expectations of the future are not realized. The problem was that AIG severely underestimated its VaR. That is, if the histogram had been constructed accurately, the x-axis for lowest 5% of profits would not be one million or less, but perhaps ten million or less. They had no idea how much money they stood to lose. Why? For two reasons.
(Reason 1: poor attention to details) It is hard to believe this is true, but AIG did not thoroughly investigate the loans it was insuring, which was like a car company not caring whether the driver was a soccer mom or a male teenager. AIG insured good loans but also some sub-prime loans, which simply refers to loans made to people with bad credit. AIG thought that of all the loans it insured, only about ten percent were sub-prime mortgages. Once they started losing money they investigated closer and discovered the true percentage was eighty-five percent!(M1)
(Reason 2: A deliberate fraud) This negligence might have been accidental, but it may have been deliberate. When a financier presents an investment opportunity to her bosses and clients she must provide the investment's VaR. The higher the VaR the less willing bosses and clients are to approve of the investment, so the ambitious financier seeks the lowest VaR possible. It is well known that many in the finance industry deliberately manipulated the calculation of their VAR to make investments look less risky than they really were. Perhaps AIG was just one among many who did so, and they intentionally underreported the amount of sub-prime loans they insured.(T1)
Like Allen Greenspan, I used to believe that financial firms were not reckless, and that no entity was more concerned with the long-run survial of the firm than the firms themselves. I was wrong, for its obsession with short-term profits (over long-term viability) caused the financial sector to attempt suicide. Of course, it's easy to attempt suicide when you know the government will stop you from dying by bailing you out! The financial sector essentially played Russian Roullette because when the chamber was empty they made lots of money and when it held a bullet the government would place the gun to taxpayers' heads instead. Government was then the problem, because past bailouts encouraged risk-taking, but government could also be the solution if they would compose smart regulations. Unfortunately, the government is barely able to understand the financial sector, much less regulate it.
Video 2—Greenspan and Bailey Were Wrong
(A.3) Trading Terminology
Every business student should understand the lingo used by firms that buy and sell financial instruments, for they are words that appear in ordinary newspapers. At a minimum, business students should be able to read The Wall Street Journal. To do this, students must understand the following.
- Traders, investors, investment banks, banks, and hedge funds—People who regularly buy and sell financial instruments like stocks, bonds, money market accounts, swaps, options, and the like are referred to as traders. It is common though not always accurate to think of traders as people who speculate on prices over short time periods, whereas investors seek financial instruments that make money over long periods. Investment banks are like banks for rich people; the wealthy park their money at the investment bank and the bank trades / investments the money on their behalf. When we heard about banks failing in 2008, it was mainly investment banks. A regular bank is where ordinary people keep their checking accounts and take out loans. Today, some banks are regular and investment banks. Unlike investment banks, regular banks are heavily regulated, and people's deposits are protected (up to a limit) by the government if the bank fails. Finally, a hedge fund is simply a smaller, aggressive investment bank that may specialize in certain types of trading. The word "hedge" in hedge funds used to mean something, but they are really more like smaller investment banks who are willing to take on considerable risks.
- Collateral—Liquid (easily sold) assets offered to secure a loan. After you have paid off the mortgage on your house you may use the house as collateral on another loan. If you default on this loan the lender then takes possession of your house. Houses can take a long time to sell and the faster it is sold the lower price the seller must accept; for these reasons homes are not liquid assets, they are illiquid assets. When traders borrow money from creditors to purchase investments they often post collateral in the form of Treasury Bonds, which can be easily sold for cash. If they cannot repay, the creditor assumes ownership of the bonds. When the government "bailed-out" banks in 2008 they typically were not bailing out the investment banks—they bailed out the creditors who lent the investment banks money.
- Leverage—The amount of money one borrows to pay for an investment. If a trader borrows $4,000 to buy a $5,000 investment, the leverage is $4,000. Often we hear of leverage-ratios which are calculated by dividing the amount of leverage by the amount of cash used to buy investments. In the previous example, the leverage-ratio is 4:1 (four dollars in leverage for every dollar in cash). Most regulations constrain traders by prohibiting leverage-ratios from exceeding a certain level.
Example
A trader wants to purchase a portfolio of stocks, expecting the
stocks to rise in value over time. The stocks cost
$1,000,000 in total. The trader borrows $950,000 (leverage) and pays the rest in cash,
for a leverage-ratio ratio of 950,000:50,000 or 19:1.
The trader wanted to borrow all $1,000,000, but regulators prohibited leverage
ratios in excess of 19:1 for this stock portfolio, based on the computed VaR for
the portfolio.
The trader may work for an investment bank, and intend to hold onto the stock
for years, or may work for a hedge fund and plan to sell the stocks again
within sixty days. While a levarage ratio of 19:1 may seem absurdly low,
regulators
would sometimes allow ratios as high as 100 to 1 and even 1,000 to 1. Generally,
though, it is my perception that a leverage-ratio of 30:1 is common.
(A.4) The Problems With VaR
(1) VaR assumes the future will resemble the past. Suppose a sophomore in college wants to guess what her GPA at graduation will be. If her GPA varied between 2.4 to 2.7 in the past, then perhaps she will simply assume that at graduation her GPA may be as low as 2.4 or as high as 2.7. That sounds sensible, and that is exactly what the histograms from which VaR is are supposed to do: to looks at the behavior of the data in the past and assumes the data will exhibit similar patterns in the future. For instance, if cattle prices tended to be between $80 and $90 per cwt in the last two years, the histograms will predict prices between $80 and $90 for next year.
VaR is an untrustworthy and dangerous measure of future market risk for one main reason: It is calculated by looking at the past...prior to the kick-starting of the crisis in mid-2007, the VaR of the big Wall Street firms was relatively quite low...A
one-day 95 percent VaR of $50 million was typical, and typically modest in its
estimation of losses: At that level, a firm would be expected to lose no more
than $50 million from its trading positions 95 percent of the time...When you consider that those Wall Street entities
owned trading assets worth several hundred billion dollars and that the eventual
setbacks amounted to several dozen billion dollars, we can appreciate that VaR’s
predictions were excruciatingly off-base.
—Pablo, Triana. 2011. The Number That Killed Us. John Wiley & Sons: NY,NY.
Note that many of the "computer models" were simply histograms.
(2) VaR predicts events with a 5% chance of occurring, but not those with a 1% chance. Remember that VaR is just a bar on a histogram, and the left-most bar in Figure 2 is set to equal 5%. It could have been set at 1% though, and would have corresponded to greater projected losses, forcing the firm to post more collateral. At 5%, the VaR indicates the losses on the fifth worst day out of every 100 days; at 1%, in indicates the losses on the worst day. If firms had chosen to calculate VaR at the 1% threshold they would have been better prepared for the 2008 Financial Crisis. Perhaps the crisis may not have occurred. Why did they choose 5% instead of 1%? To a large extent, it was because regulators approved of the 5% level and the traders wanted to assume as much risk as the regulators permitted.
And let’s not forget that VaR measures risk only up to a degree of statistical confidence (typically 95 percent or 99 percent), thus leaving out the so-called “tail events,” or those market episodes that have a lower chance of taking place. Big losses may lurk in those extremes, but that’s beyond VaR’s territory, so the model won’t register such possibilities...The most unlikely scenarios are not captured by the model, and the most unlikely scenarios may be the ones we should worry most about.
—Pablo, Triana. 2011. The Number That Killed Us. John Wiley & Sons: NY,NY.
Note that many of the "computer models" were simply histograms.
(3) Traders could calculate VaR however they liked, rendering it meaningless. Before VaR, regulators set a leverage-ratio for each class of assets based on historical data and prudent judgment. In 1996, investment firms requested the regulators allow them to use VaR calculations to set leverage-ratios instead, and the regulators happily obliged. That was not necessarily a mistake. VaR is a useful risk-management tool, if the histograms are calculated accurately. The problem is that regulators basically let firms decide how the histograms are calculated, allowing the firms to choose the data that would comprise the histograms—this let the reins loose on traders, allowing them to speculate on house prices with absurdly high leverage-ratios.
For instance, the histogram in Figure 2 was constructed with data, but sometimes a firm must make a decision about how many observations to use. If you are constructing a histogram of corn prices, do you want to use observations as far back as 1920? It hardly seems likely that the corn market in 1920 tells us anything about the corn market today. So where do you draw the line? 1950? 1974? The time period chosen is somewhat arbitrary, and firms deliberately chose sample sizes that resulted in the lowest VaR, allowing them to speculate almost exclusively with borrowed money. Not surprisingly, traders are more reckless with other people's money than their own.
It is easy for firms to design portfolios that would have exhibited little risk in the past, but that doesn't mean those portfolios will be safe in the future—just like it is easy to pick lottery numbers that would have won in the past, but almost impossible to pick numbers that will win in the future.
Figure 3—Humorous Article from The Onion
When regulators decided that VaR could be used to set leverage-ratios, they gave firms too much freedom in how to construct the histograms. It was as if the regulators said they were tired of telling traders what to do, and would now let investors hold as little collateral as possible. We all know the ending of that story.
(B) The Mathematics of Fire: An Analogy to VaR and the 2008 Financial Crisis
Once a wildfire starts officials quickly want to know where the fire might spread and how fast it may travel. In the past these forecasts were made by experienced firefighters, but as historical data on wildfires were collected and computer-power became affordable, computer models began to perform this task of divining a fire's future.
These "computer models" contain large amounts of data, equations, and algorithms. Readers may recall seeing weather maps indicating the future path of a tornado or hurricane, with an arrow showing where the hurricane is heading, and a widening arrow as it extends further into the future, indicating the meteorologists are less certain about where the hurricane will be three days from now compared to three hours from now. Just replace the hurricane with a wildfire, and you can imagine what the models are trying to accomplish. When these models are told a wildfire has started at a certain latitude and longitude, a fury of number-crunching ensues. The models already have geographic and climatic information it will use to place the fire in a proper context. It will know the current temperature, wind direction, and wind speed, suggesting where the fire is heading and at what speed. The moisture content of the surrounding forests can be predicted based off recent rainfalls and temperatures, suggesting how quickly the trees and brush might catch fire. Houses make for good fuel, and fires prefer traveling uphill to downhill; these are details the computer will incorporate into its projections.As data from more wildfires are collected, they can be used to calibrate these computer models, deliberately "tinkering" with the model to make sure it can accurately predict the path of past wildfires in hopes that will improve its ability to forecast the path of future fires. It would seem that with enough hindsight these models would prove prescient in their ability predict future fires.
Since the 1970s these computer models have earned a respected place in fire management, but lately these models are proving rather incompetent. One reason is that, like all models, it uses information on the past to predict the future, and the environment has changed so much that looking back at past wildfires tells us less about future wildfires. Mountain pine beetles are a relatively new resident of Colorado, which leaves trees drier and therefore more flammable. Because they are a new resident, the computer cannot account for them, causing them to underestimate a wildfire's true potential. The number and types of homes have changed, and some of today's bigger homes intensify fires in a way models can't predict.
As the weaknesses of computer models become increasingly apparent we are once again relying on human judgment, especially those who have spent many years on the ground fighting fires.(B1)
These computer models do a poor job of forecasting the path of a fire because they rely exclusively on historical data with no adjustments by experienced humans. Just as the computer models leave much uncertainty about the damage a wildfire may cause, VaR has proven a poor indicator of the true risk investors assume. There is nothing wrong with the theoretical construct of VaR or the computer models. They both do exactly what they were designed to do. The fault resides in how they are used. The fault resides in their human users. Just as humans cannot rely on computer models alone to judge the path of a wildfire, we were not supposed to rely on VaR alone to measure investment risk—yet it seems that is exactly what most traders did.
There is one crucial difference between the wildfire computer models and VaR. Many financial traders acted as if they were unaware of VaR's deficiencies because doing so allowed them to gamble with more of other people's money, when in fact those traders knew VaR underestimated risk. VaR was deliberately used wrongly by many. The people forecasting wildfires were honest about the weaknesses of their computer models. Investors were reckless; firefighters were not.
(C.1) Histograms: Crop Yields
As the drought of 2012 worsened, newspapers periodically reminded Americans not to worry too much about the farmers, for most of them had crop insurance subsidized by the government. Crop insurance has become the central institution for providing a safety net for American crop producers, so agribusiness students should understand how crop insurance works. In the process they will develop a foundation for studying much of modern finance.
Crop insurance does not make a farmer whole, but it makes the blow softer for crop producers. It's the large payout estimates that have some outsiders calling for changes
[because some of it is subsidized].
...
Many farmers will get paid handsomely this year...
—Fatka, Jacqui. August 13, 2012. "Crop insurance will pay big." Feedstuffs. Page 27.
The crop insurance industry uses data as fuel. These are companies that sell insurance policies to farmers, earning premiums in all years and paying big indemnities in bad years. The most important decision the companies make is the premium they charge for the policy, as it must be based on the probability of a "bad year." If this probability is overestimated they set too high a premium and don't sell many policies. If the probability is underestimated they sell policies at so low a premium they do not have enough money to pay indemnities when bad harvests arrive. Everything about an insurance company's success revolves around this probability—revolves around a histogram.
When selling crop insurance policies to protect against a bad harvest next year, the insurance company must construct histograms for yields in the coming year, a histogram which shows all possible yields and the probability of each yield being realized. The company then uses this histogram to set insurance premiums such that, on average, the money coming into the company (the premium) is greater than the money paid out by the company (indemnities). If the money coming in is greater than the money going out, on average, the company is profitable.
In this section we will study how to create an accurate and attractive histogram. Suppose we wish to take data (download here) on wheat yields in Alfalfa County and create a histogram of yields in the coming year. These data contain yields from 1970 until 2008, so let's suppose it is 2008 and we are interested in what yields could be in 2009. In the histogram of these yields, the x-axis should be intervals of yield, and on the y-axis should be the percent of past yields which reside in each interval. The x-axis intervals are referred to as "bins", and the bins are already created for you in the spreadsheet. If you construct your histogram properly it should closely resemble Figure 4, below (the red line denotes cumulative probabilities, like the probability of yield being less than 21 bushels per acre).
Figure 4—Crop Yield Histogram
(note on error: the brackets " [ " and " ( " should be switched in figure)
For help making a histogram, see this tutorial I made in Video 2. Follow it closely, because I expect you to be able to construct an exact histogram quickly.
Video 3—How To Construct A Histogram
(C.2) Histograms and Insurance
The earliest known system of insurance traces back to Rhodes in 324 BC. Purchasing a slave was a risky investment. They were not cheap, and if the slave escaped, your money spent on the slave was wasted. Slaves were also essential to an ancient economy, so Rhodes devised insurance policies where a slave owner would be reimbursed if the slave escaped. Those selling the policy charged eight percent of the price of a slave. Slaves sold for a price roughly equivalent to $3,000 U.S. dollars today. So the seller of the insurance received $3,000(0.08) = $240 each year, and would reimburse the owner $3,000 if the slave escaped.(D1)
Was this insurance policy profitable to the seller? It depends on the probability that a slave will escape. As we will see, the seller's expected profits from any one policy is: expected profits = $3,000(0.08) - $3,000(probability of escape) = $3,000(0.08 - probability of escape). So long as this probability is less than 8% the seller will profit from the policy (on average). Thus we conclude that unless the insurance was subsidized by the government, the probability of a slave escaping was less than 8%.
Since this first insurance policy, humans have bought and sold insurance concerning a variety of things, from life insurance to car insurance to health insurance for pets. Regardless of the type of insurance, the mathematical principles describing them are the same as our slave example. Companies must know the probability of an event before it can sell insurance regarding it, and today that probability is often estimated using histograms.
A histogram is what is referred to in statistics as a probability distribution. If yields in the future behave similarly to yields in the past, we can predict the probability of next year's yield being less than or equal to 21 by the percent of times past yields were less than 21.
Suppose we sell a very simple crop insurance policy that pays Alfalfa County wheat farmers $50 per acre whenever yields are less than or equal to 21 bushels per acre. Because we don't know what next year's yield will be we don't know if we will have to pay out $50 per acre. We can, however, calculate the expected payout, which is the $50 per acre times the probability yields will be less than or equal to 21. Eye-balling this probability, it seems about 2.5%.
The Expected Payout Formula
To see why the expected payout is the indemnity times the probability the
indemnity must be paid, consider a simple insurance policy where you (the
insurance company) pay someone a $1 indemnity every time they flip a coin and it
lands on heads.
You know that half the time it will land on heads and half the time on tails, so
you know that half the time you will pay $1 and half the time you will pay
nothing. If we flip the coin thousands of times and
calculate
the average payout, we know on average we will pay $0.50 (think: if you average 50,000 values of $0 and 50,000 values of $1 you will
get $0.50). This is the same as multiplying the $1 payout by the probability of flipping a heads (50%
or 0.5).
So, expected payout = (indemnity amount)(probability indemnity must be paid)
Given these considerations, we know the expected crop insurance indemnity is: ($50)(0.025)=$1.25 per acre enrolled in insurance policy (remember, yield is in dollars per acre).
If the expected indemnity is $1.25, what premium must we charge (in $ per acre) so that we expect to make money? So long as we charge more than $1.25 our expected profits are positive. For example, if we charge $2.00 per acre our expected profits are $2.00-$1.25 = $0.75 per acre. Of course, with a $2.00 premium, about 2.5% of the time the policy will lose money and 97.5% of the time it will make money, but on average the profit is $0.75 per acre.
This expected indemnity represents the breakeven premium for the insurance company. Any premium less than the breakeven premium is expected to lose money, and anything greater than this premium is expected to make money. Thus, the company will want to set a price greater than the breakeven premium of $1.25. How much higher depends on the rate at which sales drop when price rises. You can't start thinking about a good premium until you know the breakeven premium, so it is not a trivial number.
That is how insurance works. You agree to pay somebody an indemnity if an event occurs, and you charge them a premium before the event has a chance to occur. You get the premium no matter what, but only pay an indemnity if the event occurs. So long as this premium exceeds the expected payout (i.e., the breakeven premium) the policy is expected to be profitable, and to calculate this expected payout you need a histogram (or something similar to a histogram). Real insurance policies can be more complex than the one considered here, but the basics are exactly the same.
Anything can be insured. Here is a list of body parts known for sure to have been insured.
Ken Dodd’s extremely big buckteeth for $ 7.4 million!
13-year-old World Yo-Yo champion Harvey Lowe’s hands for $ 150,000!
Australia’s cricket player Merv Hughes’ walrus moustache for $ 370,000!
20th century Fox insured actress Betty Grable’s legs for $ 1 million each!
Legs of Michael Flatley of Lord of the Dance and Riverdance for $ 47 million
Food critic Egon Ronay’s taste buds for $ 400,000!
Bruce Springsteen’s voice for $ 6 million
Friendship of Bud Abbott and Lou Costello for $250,000!
Jennifer Lopez’s ass for $ 1 billion!
—How Stuffs Works. "9 Odd Things Insured by Lloyds of London." Accessed
September 10, 2013 at http://money.howstuffworks.com/personal-finance/financial-planning/9-odd-things-insured-by-lloyds-of-london.htm#page=0.
Figure 5—If it's valuable, insure your hair
(C.3) Histograms: Historical Simulation
Histograms can be particularly useful for a business wishing to determine the probability of a new venture, because it often allows them to ask the question, "What if I had participated in this venture in the past?" If the venture would have been profitable in the past that is a positive sign it would be profitable in the future. To illustrate, suppose it is 2008 and you are considering whether you should use your savings to purchase stocks or bonds. In that year stocks lost much of their value while bonds performed relatively well, and if the world in 2008 was all that mattered purchasing bonds (not stocks) would seem the wise choice.
At the same time it is obvious that 2008 is not the only year that should matter, especially if you plan to keep those savings in stocks or bonds for the next twenty years as part of your retirement plan. This is a case where it is useful to ask what if you had put all your money in bonds in the previous twenty years, and what if you had your money in stocks instead. Maybe twenty years isn't enough, and you are curious how stocks and bonds performed in the last 60 years. It is relatively easy to find financial tools with data on the historical performance of stocks and bonds, like this one I used to construct Figure 5.
Figure 6—Stocks, Bonds, and Cash Account Returns (1950-2010)(A1)
There is no doubt that investing in the stock market over the previous 60 years was highly preferable to the bond market. It them seems reasonable to assume that stocks will earn more money in the future also. This thought experiment, where we ask what would have happened if we performed some action in the past, is what we call historical simulation. We simulate a past that could have occurred using historical data.
Section (C.2) of this article was also a historical simulation. To estimate the expected cost of an insurance policy a histogram of past yields was estimated and used to compute what the policy would have cost the insurance company to administer in the past. A policy that paid farmers $50 per acre when yields are 21 bushels per acre or less, if the policy had been sold between the years 1970 and 2008, would have cost the company $1.25 per acre on average. Assuming future yields will resemble historical yields, the policy is also expected to cost the company $1.25 per acre in the future, if the policy is sold.
Historical simulation is popular with businesses because it requires very little statistical knowledge and in some cases provides accurate answers. To predict the future costs of an insurance policy, all we needed in (C.2) were historical data and knowledge on how to make a histogram. At no point did we calculate averages, standard deviations, or t-values; nor did we conduct a hypothesis test or consult a z-table. All historical stimulation requires is some Excel experience and a logical mind—as well as wise judgments about when the past can provide good insights into the future. Unfortunately, the lack of such wise judgments causes many businesses to suffer, and helped cause the 2008 Financial Crisis.
References
(A1) Activainteractive. Portfolio Growth-Historical Returns. Accessed August 16, 2012 at http://www.ativa.com/web-calculators/portfolio-growth/
(B1) Behar, Michael. September 1, 2012. "Burning Question: Why Are Wildfires Defying Long-Standing Computer Models?" The Atlantic.
(D1) Durant, Will. The Story of Civiliation. Part II. The Life of Greece. Chapter XXIII: Greece and Macedon. Page 558.
(M1) Mclean, Bethany and Joe Nocera.2010. All The Devils Are Here. Portfolio/Penguin: NY, NY.
(T1) Triana, Pablo. 2011. The Number That Killed Us: A Story of Modern Banking, Flawed Mathematics, and a Big Financial Crisis. Wiley Publisher: NY, NY.
