October 2012

Measures of Risk ~ Equity & Debt

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Measures of Risk, Performance, Mutual Funds , Stocks, Standard Deviation, Variance, Beta, Modified duration, Credit Risk, Interest Rate Risk, Weighted Average Maturity  ,Yield Spread,

Investors generally focus on the returns of any asset. They largely ignore the risk factors and most importantly are ignorant of the measures of risk. 

And so, the real Risk comes from not knowing what they are doing ~ Warren Buffett

This post talks about the measures of risks in equities & debt. The awareness of the measures of risk is extremely helpful in designing a comprehensive financial plan, investing, asset allocation etc.

Fluctuation in returns is used as a measure of risk.

Therefore, to measure risk, generally the periodic returns (daily / weekly / fortnightly / monthly) are first worked out, and then their fluctuation is measured.

The fluctuation in returns can be assessed in relation to itself, or in relation to some other index. Accordingly, the following risk measures are commonly used.

Variance

Suppose there were two stocks, with monthly returns as follows: Stock 1: 5%, 4%, 5%, 6%. Average=5%  & Stock 2: 5%, -10%, +20%, 5% Average=5%

Although both stocks have the same average returns, the periodic (monthly) returns fluctuate a lot more for Stock 2. Variance measures the fluctuation in periodic returns of a asset, as compared to its own average return. This can be easily calculated in MS Excel using the following function:

=var(range of cells where the periodic returns are calculated)

Variance as a measure of risk is relevant for both debt and equity.

Standard Deviation

Like Variance, Standard Deviation too measures the fluctuation in periodic returns of a scheme in relation to its own average return. Mathematically, standard deviation is equal to the square root of variance.

This can be easily calculated in MS Excel using the following function: =stdev(range of cells where the periodic returns are calculated)

Standard deviation as a measure of risk is relevant for both debt and equity schemes.

Beta

Beta is based on the Capital Assets Pricing Model, which states that there are two kinds of risk in investing in equities – systematic risk and non-systematic risk.

Systematic risk is integral to investing in the market; it cannot be avoided. For example, risks arising out of inflation, interest rates, political risks etc.

Non-systematic risk is unique to a company; the non-systematic risk in an equity portfolio can be minimized by diversification across companies. For example, risk arising out of change in management, product obsolescence etc.

Since non-systematic risk can be diversified away, investors need to be compensated only for systematic risk. This is measured by its Beta.

Beta measures the fluctuation in periodic returns in a scheme, as compared to fluctuation in periodic returns of a diversified stock index over the same period.

The diversified stock index, by definition, has a Beta of 1. Companies or schemes, whose beta is more than 1, are seen as more risky than the market. Beta less than 1 is indicative of a company or scheme that is less risky than the market.

Beta as a measure of risk is relevant only for equity schemes.

Modified Duration

This measures the sensitivity of value of a debt security to changes in interest rates. Higher the modified duration, higher the interest sensitive risk in a debt portfolio.

The returns in a debt portfolio are largely driven by interest rates and yield spreads.

Interest Rates

Suppose an investor has invested in a debt security that yields a return of 8%. Subsequently, yields in the market for similar securities rise to 9%. It stands to reason that the security, which was bought at 8% yield, is no longer such an attractive investment.

It will therefore lose value. Conversely, if the yields in the market go down, the debt security will gain value. Thus, there is an inverse relationship between yields and value of such debt securities which offer a fixed rate of interest.

A security of longer maturity would fluctuate a lot more, as compared to short tenor securities. Debt analysts work with a related concept called modified duration to assess how much a debt security is likely to fluctuate in response to changes in interest rates.

In a floater, when yields in the market go up, the issuer pays higher interest; lower interest is paid, when yields in the market go down. Since the interest rate itself keeps adjusting in line with the market, these floating rate debt securities tend to hold their value, despite changes in yield in the debt market.

If the portfolio manager expects interest rates to rise, then the portfolio is switched towards a higher proportion of floating rate instruments; or fixed rate instruments of shorter tenor. On the other hand, if the expectation is that interest rates would fall, then the manager increases the exposure to longer term fixed rate debt securities.

The calls that a fund manager takes on likely interest rate scenario are therefore a key determinant of the returns in a debt fund – unlike equity, where the calls on sectors and stocks are important.

Yield Spreads

Suppose an investor has invested in the debt security of a company. Subsequently, its credit rating improves. The market will now be prepared to accept a lower yield spread. Correspondingly, the value of the debt security will increase in the market.

A debt portfolio manager explores opportunities to earn gains by anticipating changes in credit quality, and changes in yield spreads between different market benchmarks in the market place.

Weighted Average Maturity

While modified duration captures interest sensitivity of a security better, it can be reasoned that longer the maturity of a debt security, higher would be its interest rate sensitivity. Extending the logic, weighted average maturity of debt securities in a scheme’s portfolio is indicative of the interest rate sensitivity of a scheme.

Being simpler to comprehend, weighted average maturity is widely used, especially in discussions with lay investors. However, a professional debt fund manager would rely on modified duration as a better measure of interest rate sensitivity. 

More on Mutual Funds

How do you compare and evaluate Mutual Fund Performance

 Risk-adjusted Returns, Evaluating Mutual Fund Performance, Sharpe Ratio, Treynor Ratio, Beta, Alpha, tracking error, Index funds, .

Risk-Adjusted Return is one of the concept investors should be aware when comparing returns of mutual funds.  

One way of comparing the returns between two different funds is to look at the their relative returns over a period. However, a weakness of this approach is that it does not differentiate between two schemes that have assumed different levels of risk in pursuit of the same investment objective.

It is possible that although two schemes share the benchmark, their risk levels will differ, and sometimes quite dramatically as well. Evaluating performance, purely based on relative returns, may be unfair towards the fund manager who has taken lower risk but generated the same return as a peer.

An alternative approach to evaluating the performance of the fund manager is through the risk reward relationship.

The underlying principle is that return ought to be commensurate with the risk taken.

A fund manager, who has taken higher risk, ought to earn a better return to justify the risk taken. A fund manager who has earned a lower return may be able to justify it through the lower risk taken. Such evaluations are conducted through Risk-adjusted Returns.

There are various measures of risk-adjusted returns. We’ll look at the three most commonly used :

Sharpe Ratio

An investor can invest with the government, and earn a risk-free rate of return (Rf). T-Bill index is a good measure of this risk-free return.

Through investment in a scheme, a risk is taken, and a return earned (Rs).

The difference between the two returns i.e. Rs – Rf is called risk premium. It is like a premium that the investor has earned for the risk taken, as compared to government’s risk-free return.

This risk premium is to be compared with the risk taken. Sharpe Ratio uses Standard Deviation as a measure of risk. It is calculated as

(Rs minus Rf) ÷ Standard Deviation

Thus, if risk free return is 5%, and a scheme with standard deviation of 0.5 earned a return of 7%, its Sharpe Ratio would be (7% – 5%) ÷ 0.5 i.e. 4%.

Sharpe Ratio is effectively the risk premium per unit of risk. Higher the Sharpe Ratio, better the scheme is considered to be. Care should be taken to do Sharpe Ratio comparisons between comparable schemes. For example, Sharpe Ratio of an equity scheme is not to be compared with the Sharpe Ratio of a debt scheme.

Treynor Ratio

Like Sharpe Ratio, Treynor Ratio too is a risk premium per unit of risk.

Computation of risk premium is the same as was done for the Sharpe Ratio. However, for risk, Treynor Ratio uses Beta.

Treynor Ratio is thus calculated as: (Rf minus Rs) ÷ Beta

Thus, if risk free return is 5%, and a scheme with Beta of 1.2 earned a return of 8%, its Treynor Ratio would be (8% – 5%) ÷ 1.2 i.e. 2.5%.

Higher the Treynor Ratio, better the scheme is considered to be. Since the concept of Beta is more relevant for diversified equity schemes, Treynor Ratio comparisons should ideally be restricted to such schemes.

Alpha

The Beta of the market, by definition is 1. An index scheme mirrors the index. Therefore, the index scheme too would have a Beta of 1, and it ought to earn the same return as the market. The difference between an index fund’s return and the market return, as seen earlier, is the tracking error.

Non-index schemes too would have a level of return which is in line with its higher or lower beta as compared to the market. Let us call this the optimal return.

The difference between a scheme’s actual return and its optimal return is its Alpha – a measure of the fund manager’s performance. Positive alpha is indicative of out-performance by the fund manager; negative alpha might indicate under- performance.

Since the concept of Beta is more relevant for diversified equity schemes, Alpha should ideally be evaluated only for such schemes.

These quantitative measures are based on historical performance, which may or may not be replicated.

Such quantitative measures are useful pointers. However, blind belief in these measures, without an understanding of the underlying factors, is dangerous. While the calculations are arithmetic – they can be done by a novice; scheme evaluation is an art – the job of an expert. 

Source : NISM
 
More on Mutual Funds

May 2012

Options Delta : The Basics

options, call, put, hedging, risk , return, delta, delta neutral strategy, options basics, enrichwise

Options Delta is the ratio of the change in the price of the stock option to the change in the price of the underlying stock

Delta = instantaneous change in value of asset with respect to an underlying risk factor. Option’s delta changes continuously as underlying risk factor changes

Here are some basic characteristics of Options Delta :

  • It is the change in the price of an option for a one point moves in the underlying
  • Delta of a call option is positive
  • Delta of a put option is negative
  • Delta increases – in decreasing index
  • Delta decreases – in increasing index
  • Call options: 0 < Option Delta < 1
  • Put options: -1 < Option Delta < 0
  • In-the-money options: Delta Option approaches 1 (call:+1,put:-1)
  • At-the-money options: Delta is about 0.5 (call:+0.5, put: -0.5)
  • Out-of-the-money options: Delta Option approaches 0
  • Call Option Delta can be interpreted as the probability that the option will finish in the money
  • An at-the-money option : which has a delta of approximately 0.5, has roughly a 50/50 chance of ending up in-the-money
  • Put Option Delta can be interpreted as -1 times the probability that the option will finish in the money

Impact of Time : As time passes, the delta of In-the-money options: increases & Out-of-the-money options: decreases

Impact of Volatility : As volatility falls, the delta of In-the-money options: increases & Out-of-the-money options: decreases

Hedging using Options – Delta to neutralize market risk :

  • In order to maintain a riskless hedge using an option and the underlying stock, need to adjust holdings in the stock periodically
  • An important parameter in pricing and hedging of options
  • No. of units of stock should hold for each option shorted in order to create a riskless hedge
  • Construction of a riskless hedge is sometimes referred as delta hedging

To get more information on Options Greeks , read Options Basics of Vega ,  Gamma 

“The greatest ignorance is to reject something you know nothing about”…If you are invested in Markets, it makes sense to be aware of & have an idea about Options