Volatility and Risk Volatility Definition In finance, volatility is a statistical measurement of up and down asset price fluctuations over time. If an asset has rapid dramatic price swings, volatility will be high. If prices are consistent and rarely change, volatility is low. Volatility can be measured as the annualized standard deviation.
Volatility as Measure of Risk Volatility is often used to measure risk. Many common measurements of risk, such as beta, utilize volatility in calculations. It makes sense that an asset that has had huge price swings is more risky than an asset that is not volatile.
Upside vs. Downside Volatility However, the actual effectiveness of using volatility as a measurement of risk is questionable. The main imperfection of volatility is that it does not differentiate upside and downside price movements. For example, assume a stock decreased in price from $10 to $2. Also assume that the stock exhibited low volatility before this price decrease. In this example, volatility was lower when the stock price was $10 then when the stock price was $2. If volatility was being used a measure of risk in this example, then when the stock priced at $10 it would have been less risky. This assumption is not logical.
Limitations of Predictions In addition, volatility is a measurement over time that relies on historical data. Past events, however, do not guarantee future results. Using historical volatility as a predictive measure of future risk is thus limited by the uncertainty of future returns. In the financial markets, somewhat unpredictable future returns and radical events are especially prevalent.
Despite imperfections, estimating risks using volatility an important part of risk managements, but the predictive limitations of the measurements needs to be considered.
Famous Quotes About Volatility and Risk
"The true investor welcomes volatility. Ben Graham explained why in Chapter 8 of The Intelligent Investor. There he introduced "Mr. Market," an obliging fellow who shows up every day to either buy from you or sell to you, whichever you wish. The more manic-depressive this chap is, the greater the opportunities available to the investor. That's true because a wildly fluctuating market means that irrationally low prices will periodically be attached to solid businesses. It is impossible to see how the availability of such prices can be thought of as increasing the hazards for an investor who is totally free to either ignore the market or exploit its folly." - 1993 Shareholders Letter by Warren Buffet
"Berkshire's whole record has been achieved without paying one ounce of attention to the efficient market theory in its hard form. And not one ounce of attention to the descendants of that idea, which came out of academic economics and went into corporate finance and morphed into such obscenities as the capital asset pricing model, which we also paid no attention to. I think you'd have to believe in the tooth fairy to believe that you could easily outperform the market by seven-percentage points per annum just by investing in high volatility stocks. Yet many people still believe it. But Berkshire never paid any attention to it." - Charlie Munger
VIX - The CBOE Volatility Index VIX, often referred to as the investor fear guage, is the ticker symbol for the Chicago Board Options Exchange(CBOE) Volatility Index. The VIX is based on implied volatility of a wide variety options available on the S&P 500 index and is calculated in real time by the CBOE. This index allows expected volatility to be traded through the use of futures. There are also other variations of the VIX. The VXD tracks the Dow Jones Industrial Average. The VXN tracks the Nadsaq 100 index.
Fat Tails and Limitations of Normal Distirbutions Normal distributions (a bell curve) of asset returns is a key assumption made by many financial models, including the capital asset pricing model(CAPM) and the Black-Scholes option pricing model(BSM). However, actual asset returns may not be so normal.
Normal Distributions Overestimate the Improbability of Unlikely Market Events Using a normal distribution, events that diverge from the mean by five or more standard deviations, known as a five-sigma event, are very rare and ten-sigma events are nearly impossible. For example, the 1987 market plunge represents a change equalling 22 standard deviations. The odds of such a 22 standard deviation event occurring are 10^50. However, events deemed nearly impossible by models assuming normal asset return distributions are possible in the financial markets and do occur. In fact, there have been multiple fluctuations greater than five standard deviations. Thus, dramatic market swings do occur in a greater frequency than is possible assuming normal distributions suggesting distributions are not normal.
Fat Tail Definition Fat tails are statistical irregularities, in which very low and high values are more frequent than a normal distribution predicts. In a normal distribution, the tails to the extreme left and extreme right of the mean become smaller, ultimately reaching zero occurrences. However, some real life statistical series demonstrate occurrences of low and high values that are greater than theoretically expected by a normal distribution. These irregular occurrences or extreme events are described as fat tails.
Possible Reasons Why Fat Tails Exist in Financial Markets The randomness associated with normal distributions may not completely reflect the financial markets. The central reasons why fat tails exist is a result of interdependence during market extremes. People's decisions are not always fully independent or logical. At extreme market highs, investors become irrationally exuberant. At extreme lows, investors become fearfull and less risk tolerant. Because of interdependence and influence of aspects of behavioral finance, people buy at illogical highs and sell and ludicrous lows. Illogical and non random events push markets to extremes more frequently than models assuming complete randomness and normal distributions would predict.
Fat tails are an important concept for modeling returns and estimating risk. Fat tails reinforce the idea that past results do not guarentee future results. The risk of extreme price changes are often higher than they appear. Many investors do not take into account these unsuspected risks.
"By far the most significant event in finance during the past decade has been the extraordinary development and expansion of financial derivatives. These instruments enhance the ability to differentiate risk and allocate it to those investors most able and willing to take it - a process that has undoubtedly improved national productivity growth and standards of living." -Alan Greenspan
Financial derivatives are financial instruments that "derive" value from an underlying item such as an asset or index. The use of derivatives provides exposure to the linked underlying item without necessitating the trade or exchange of the item itself. This allows specific risks, such as commodity or equity price fluctuations, to be traded in financial markets. Derivatives may be traded on exchanges such as the New York Stock Exchange(NYSE) and Chicago Mercantile Exchange(CME). Every derivative has unique features and provisions, and each derivative is used for a special financial purpose.
Derivative Uses The main purposes of derivatives are hedging or providing risk reduction, arbitrage, and speculation. Derivatives allow risk of the underlying asset or index to be transferred between entities. This permits intermediary financial institutions and other entities that are more capable or knowledgeable about the specific risk to manage these risks.
For example, a corn farmer may enter into a derivative contract (normally a futures contract) to reduce risk from corn price fluctuation. If the farmer fears the price will fall below a hypothetical production price of $2 per bushel, the farmer may enter into a derivative contract with a merchant that agrees to purchase the corn at a specific price when the crop is harvested in a specific amount of time. In this case, assume the merchant agrees in the derivative contract to purchase corn at $2.5 per bushel. By utilizing derivatives, the farmer has guaranteed a corn sale price of $2.5 per bushel. If the price of corn decreases in the future, the value of the derivative contract increases as the farmer is able to sell corn above the market price. The use of the derivative allows the farmer to hedge the risk of a corn price decrease, and the speculator accepts this risk because of the possibility of a large reward if the price of the corn rises above $2.5 per bushel.
Derivatives are also used for arbitrage and speculation. Arbitrage is the practice of taking advantage of differences in price in two or more markets. For example, if a commodity was being sold for a lower price in a rural area than in a city, the arbitrageur could purchase the lower cost commodity in the rural area and sell it at a higher price in the city. This example excludes extra costs, such as transportation costs, that are not present in "true" arbitrage that requires no additional risk. Derivative traders engaging in arbitrage may seek opportunities between different derivatives of identical or related securities. For example, if the price of a stock listed on the NYSE is different than the corresponding futures contract on the (CME) an arbitrageur could purchase the less expensive item and sell the more expensive item.
Enhanced exposure and reward potential are the primary reasons why derivatives are used for speculation. The use of options, for example allows for greater returns than the actual price movement of the underlying asset or index. For example, if a trader purchased a stock for $20 per share and the price increased to $40 per share, the trader would have a 100% return. If the same trader instead paid a $1 option premium to purchase the stock at $21 per share, the trader would have earned an 1800% return ((40-21-1)*100%). The use of derivatives allows for greater reward potential. In addition, derivatives allow traders or investors to gain exposure to underlying assets or indexes when the direct ownership of these underlying items is difficult.
Main Derivative Contract Types Swaps - Two entities exchange cash flows Options - Contracts give holder the right but not the obligation to buy or sell an asset as a specific future date Futures - Contracts buy buy or sell an asset at a specific future date.
Please continue to check the Sharpe Investing blog for future new posts about these specific derivative contract types.
Sharpe Ratio The Sharpe Ratio is a formula used to measure risk/return. The ratio describes the amount of extra return received for the extra volatility of a more risky asset. The higher the Sharpe Ratio, the greater returns are for each unit of risk. The Sharpe Ratio is calculated by subtracting the risk free rate or return from the return of the portfolio and then dividing by the portfolio's standard deviation. By using the Sharpe Ratio, investors can theoretically compare risk adjusted returns of investments or portfolios that have different returns and risk levels. The higher the ratio is the better.
Formula
E = Expected Value R = Expected Portfolio Return Rf = Risk Free Rate
The numerator of the ratio is the expected return that an asset is expected to provide above the risk free rate.
The denominator is the portfolio's standard deviation. Standard deviation is the square root of the variance of the portfolio. Possible outcomes fall within standard deviations. Possible returns are most likely within one standard deviation. Two standard deviations covers about 95% of observations. Three standard deviations account for over 99% of observations.
Note:Images and historic Sharpe Ratios reported from second hand source. Discussion about these and other figures can be viewed here.
Sharpe Ratio Problems or Limitations The Sharpe Ratio is a very useful statistic for portfolio or investment comparison. However, like many aspects of finance and investing the ratio has problems and limitations.
The Sharpe Ratio uses standard deviation as a measure of volatility. Some argue, however, that standard deviation is not a proper measure of volatility. Standard deviation is only a rough proxy for a non definite concepts such as risk.
The Portfolio return component of the Sharpe Ratio assumes or requires that returns are normally distributed. However, the markets are subject to many abnormalities, such as fatter tails, that can skew this normal distribution, thus limiting the Sharpe Ratio's accuracy.
Future market uncertainty also limits the Sharpe Ratio. Historic Sharpe Ratios are calculated using returns and standard deviations over previous periods. While historic data can provide a good general idea of trends and values, past performance is no guarantee of future results. Forward-looking Sharpe Ratios are based on projections which also are limited by future uncertainty.
Sharpe Ratio calculation needs to be adjusted for portfolio analysis. Using the Sharpe Ratio to directly compare two investments as the basis for adding one to a portfolio is not entirely correct. The Sharpe Ratio may be inaccurate if one or more of the investments is highly correlated with other investments in the portfolio. The solution to this problem is to construct different Sharpe Ratios for different portfolios.
Conclusion The Sharpe Ratio is an important statistic for measuring risk adjusted returns, comparing alternative portfolios, and comparing similar investments. Although the ratio has limitations, the Sharpe Ratio is still a very important tool for investment comparison and analysis.
Read John Bogle's Opinion of the Sharpe Ratio in this excerpt from Common Sense on Mutual funds. Thu, 07 Jun 2007 23:05:00 +0000
Sortino Ratio The Sortino ratio is a financial ratio, similar to the Sharpe ratio, that measures the risk-adjusted return of investments or portfolios. Unlike the Sharpe ratio, the Sortino uses downside-volatility(sometimes referred to as semi-volatility) as the denominator instead of standard deviation. The use of downside-volatility allows the Sortino ratio to measure the return of "negative" volatility.
Downside deviation differentiates "positive" volatility from "negative" volatility, unlike standard deviation. Standard deviation is the square root of volatility. However, using standard deviation as a measure of risk may not be completely accurate. For example, assume investment A has a return of 10% in year one and -10% in year two. Investment B has a 0% return in year one and a 20% return in year two. The total variance in these investments is the same, 20%. However, investment B is obviously more favorable. Because the Sharpe ratio measures risk using standard deviation, the Sharpe ratio does not differentiate between positive and negative volatility.
S=(R-T)/DV
R = Asset or Portfolio return T = Minimum Acceptable Return DV = Downside-Volatility
The Sortino Ratio differentiates between this positive and negative volatility by replacing standard deviation with downside-volatility. Downside-volatility is the volatility of returns below a minimal acceptable return (MAR). The MAR is usually set at 0%. Distribution of returns is analysed below this MAR. The denominator of the Sortino ratio is calculated only with data from periods where performance was below the set MAR. This differentiates the "positive" and "negative" volatility.
Large Sortino Ratios indicate a low risk of large losses occurring and should be considered more by risk conscious investors.
Historic Sortino Ratios
Note:Data compiled from same source as Historic Sharpe Ratios. See Sharpe Ratio post for more information. Sat, 09 Jun 2007 06:41:00 +0000
Irrational Exuberance Irrational Exuberance, by Yale economist Robert J. Shiller, details historical indicators of stock market bubbles. The following is a list of these indicators.
2. High PE ratios. When the market reaches PE ratio extremes on the high or low end there is a reversion to the mean. The pattern of market bubbles to be linked with high PE ratios is illustrated by the first graph above. Note the very high PE ratios in the 2000 bubble. To cause PE ratios to return to the average, prices must fall faster than earnings or earnings must rise faster than prices.
The trend in S&P 500 price and PE ratios is an inverse relationship. The graph above illustrates that periods of low S&P PE ratio were followed by periods of greater price increase than periods with high S&P PE ratios.
3. Increasingly optimistic analyst forecasts.
4. Increasing or high public market optimism.
5. Increasing market interest and greater volume of financial news
6. Creation of more investment clubs than average. This data is measured by the NAIC. This chart shows the growth in the number of investment clubs. Peaks are present at many market bubbles.
7. Rise in volume of shares traded.
8. New era thinking. In many historic bubbles, technological advances caused people to think that they were an a "new era" that rationalized the dramatic increase in stock market prices.
9. Growth not supported by earnings growth.
This information was extrapolated from Irrational Exuberance. It is important to note that many of these factors seem to be interrelated. The book also has other interesting ideas. One of the explanations for dramatic market increases was the feed back loop. Consistent price increases cause people to buy stock which increases the price causing the pattern to repeat. Bull market indicators were also extrapolated from the book. Some indicators were, important new technology and government changes supporting the market system. Tue, 05 Jun 2007 15:58:00 +0000
Warren Buffet CNBC Interview Warren Buffet is considered the most successful investor. Studying the methods, ideology, and background of this great investor is important. CNBC interviewed Buffet in the interesting segment posted below. Buffet's prospective on investing and life are unique and refreshing. Below are the video segments posted on YouTube.com. The first segment is located on top, directly below, followed by the remaining semgments in order.
Mortgage-Backed Securities A Mortgage-Backed security(MBS) is a debt obligation (bond) that represents claims to the cash flows from pools of mortgage loans. Mortgage providers sell the loans to an Agency or company that packages or pools loans together for sale to investors, creating a MBS. As the loans are paid, the MBS owner receives payments of interest and principle. Because mortgagors are have the option to pay more than the required monthly payment(curtailment) or pay off the loan in its entirety(prepayment)the monthly cash flow is not completely known in advance, increasing risk. Mortgage-Backed Securities are purchased at issuance or in the secondary market.
Most Mortgage-Backed Securities are issued by the Government National Mortgage Association (Ginnie Mae), the Federal National Mortgage Association (Fannie Mae), or the Federal Home Loan Mortgage Corporation (Freddie Mac). Ginnie Mae is a U.S. government agency backed by the full faith and credit of the U.S. government. Ginnie Mae guarantees that investors receive timely payments. Fannie Mae and Freddie Mac are U.S. government-sponsored agencies that also provide certain guarantees and have special authority to borrow from the U.S. Treasury. Some other private institutions, such as banks, brokerage firms,and home builders, also securitize mortgages, called as "private-label" Mortgage-Backed securities.
Mortgage Pass-Through The most common form of a MBS is a mortgage pass-through. In this structure, payments of principle and interest (less service charge) from the loan pool are passed directly to investors each month.
In a fixed rate residential mortgage, the mortgagor makes a fixed payment each moth until maturity. This payment includes the principle and the interest. As time progresses, the interest portion of the monthly payment decreases because as the principle is paid off, the size of the interest payment declines.
When the mortgage holder exercises the option of prepaying their mortgage, this principle payment is passed through to the MBS holder. Although the MBS holder receives a larger cash payment, the MBS holder will not receive the future interest payments from the loan. Prepayments thus create risk in the market(prepayment risk) and uncertainty in future cash flows of the MBS.
Collateralized Mortgage Obligation (CMO) In a CMO, different bond classes are issued, which participate in different components (tranches) of the net cash flows from the mortgage pool. A CMO is any one of those bonds. The tranches are structured to each have their own maturity range and risk characteristics, allowing investors to select bonds that better meet their needs. Collateral for the securitization may represent a pool of mortgages, but it is often a mortgage pass-through.
The most basic way a mortgage loan can be transformed into a bond suitable for purchase by an investor would simply to be to "split it". For example, a $300'000 30 year mortgage with an interest rate of 6.5% could be split into 300 1000 dollar bonds. These bonds would have a 30 year amortization, and an interest rate of 6.00% for example (with the remaining .50% going to the servicing company to send out the monthly bills and perform servicing work). However, this format of bond has various problems for various investors
Even though the mortgage is 30 years, the borrower could theoretically pay off the loan earlier then 30 years, and will usually do so when rates have gone down, forcing the investor to have to reinvest his money at lower interest rates, something he may have not planned for. This is known as prepayment risk.
A 30 year time frame is a long time for an investor's money to be locked away. Only a small minority of investors would be interested in locking away their money for this long. Even if the average home owner refinanced their loan every 10 years, meaning that the average bond would only last 10 years, there is a risk that the borrowers would not refinance, such as during an extending high interest rate period, this is known as extension risk. In addition, the longer time frame of a bond, the more the price moves up and down with the changes of interest rates, causing a greater potential penalty or bonus for an investor selling his bonds early. This is known as interest rate risk.
Most normal bonds can be thought of as "interest only loans", where the bond issuer borrows a fixed amount and then pays interest only before returning the principal at the end of a period. On a normal mortgage, interest and principal is paid each month, causing the amount of interest earned to decrease. This is undesirable to many investors because they are forced to reinvest the principal.
On loans not guaranteed by the quasi-governmental agencies Fannie Mae or Freddie Mac, certain investors may not agree with the risk reward tradeoff of the interest rate earned versus the potential loss of principal due to the borrower not paying.
Salomon Brothers and First Boston created the CMO concept to address these issues. A CMO is essentially a way to create many different kinds of bonds from the same mortgage loan so as to please many different kinds of investors. For example:
A group of mortgages could create 4 different classes of bonds. The first group would receive any prepayments before the second group would, and so on. Thus the first group of bonds would be expected to pay off sooner, but would also have a lower interest rate. Thus a 30 year mortgage is transformed into bonds of various lengths suitable for various investors with various goals.
A group of mortgages could create 4 different classes of bonds. Any losses would go against the first group, before going against the second group, etc. The first group would have the highest interest rate, while the second would have slightly less, etc. Thus an investor could choose the bond that is right for the risk they want to take (ie. a conservative bond for an insurance company, a speculative bond for a hedge fund).
A group of mortgages could be split into principal only and interest only bonds. The principal only bonds would sell out a discount, and would thus be zero coupon bonds (ie bonds that you buy for 800 dollars a piece and which mature at 1000 dollars, without paying any cash interest). These bonds would satisfy investors who are worried that mortgage prepayments would force them to reinvest their money at the exact moment interest rates are lower. The interest payments would be sold off as interest only bonds. These kinds of bonds would dramatically change in value based on interest rate movements, allowing them to be used as an insurance against the changes in other bonds prices. Striped Mortgage-Backed Securities (SMBS) Stripped mortgage securities, first introduced in 1986, are created by segregating the cash flows from the underlying mortgage loans or mortgage securities to create two or more new securities, each with a specified percentage of the underlying security’s principal payments, interest payments or a combination of the two. For example, the cash flow on an 8 percent pass-through security might be redistributed to create one new security with a 10 percent coupon and another security with a 6 percent coupon.
Securities may be partially stripped so that each investor class receives some interest and some principal. When securities are completely stripped, all the interest is distributed to one type of security, known as interest-only (IO), and all the principal distributed to another, known as principal-only (PO). These securities may be custom-made to suit individual portfolio needs, depending on which portion of the cash flow the investor wants. Strips, IOs and POs can be created in a pass-through structure or as tranches of a CMO.
The market values of IOs and POs are very sensitive to fluctuations in prepayment rates and interest rates, making them more volatile than standard pass-throughs. As with most fixed-income securities, POs, for example, increase (or decrease) in value as interest rates decline (or rise). For this reason, the investors in these securities are primarily institutional.
Price behavior also depends on whether the mortgage collateral was purchased at a premium or a discount to its par value. Prepayments on discount coupon POs generally are much lower than prepayments on premium coupon POs.
On the other hand, IOs increase (or decrease) in value as interest rates rise (or decline). Since prepayment rates generally decrease as interest rates rise, investors in IOs are likely to receive interest payments over a longer time period, thus increasing the value of their investment. However, in a low-interest-rate, high-prepayment environment, the market value of an IO may decline considerably, and an investor may not recoup his or her initial investment. IOs can function as portfolio hedging vehicles, because prepayments cause the value of an IO strip to move in the opposite direction from many other mortgage and fixed-income securities.
Risks Prepayment Risk – Changes in the prepayment speeds of the underlying mortgages will have a direct impact on the maturity structure of the pass-through security. An increase in prepayment speeds will lead to acceleration in principal returns and a contraction in the average life. A drop in prepayments, on the other hand, will lead to a slow down in principal returns and an extension in the average life.
Change in interest rates is the driving factor in the number of prepayments. As interest rates decline, fixed-rate mortgage holders are more likely to refinance mortgages to take advantage of the lower rates which would lower monthly mortgage payments. This is detrimental to MBS holders because, principle is normally returned to investors when reinvestment rates are unattractive, and not returned when reinvestment rates are attractive. MBS have higher yields than comparable fixed income instruments to compensate for prepayment risk.
Interest Rate Risk – Like any other fixed-income instrument, mortgage pass-through securities bear exposure to interest rate risk. For example, if principal returns on a mortgage security accelerate because interest rates are trending downward, the average life will contract and interest payments will be received over a shorter period of time. Conversely, if interest rates increase, return of principal can decelerate, causing the security's average life to extend. In either case, changes in the level of interest rates can directly affect a mortgage security's market value and total return.
Spread Risk – The yield spreads between Treasury and mortgage securities fluctuate on a daily basis. If the yield spread on a mortgage security widens versus Treasuries, an investor seeking to liquidate a position could suffer a capital loss, even if the Treasury market is virtually unchanged.
There are also differences between different MBS, resulting from the type of underlying mortgage and demographic or socioeconomic factors.
