Modified Duration of   Bonds

Posted by Prashant Shah on February 26, 2011

There is an inverse relationship between price and yield. What should be the change in price with a change in yield? It can be answered with the help of duration concept and especially with modified duration. Modified duration is a modified version of the Macaulay model that accounts for changing interest rates. Modified formula shows how much the duration changes for each percentage change in yield. There is an inverse relationship between modified duration and an approximate 1% change in yield. The calculation of the same is as follows:

Where ‘f’ is frequency of payment of coupon

Bond Duration Analysis for CFP –   1

Posted by Prashant Shah on January 16, 2013

In the case of bonds with a fixed term to maturity, the tenor of the bond is a simple measure of the time until the bond’s maturity. However, if the bond is coupon paying, the investor receives some cash flows prior to the maturity of the bond. Therefore it may be useful to understand what the ‘average’ maturity of a bond, with intermittent cash flows.

Since the coupons accrue at various points in time, it would be appropriate to use the present value of the cash flows as weights, so that they are comparable. Therefore we can arrive at an alternate measure of the tenor of a bond, accounting for all the intermittent cash flows, by finding out the weighted average maturity of the bond, the present value of cash flows being the weightage used. This technical measure of the tenor of a bond is called duration of the bond.

Duration is defined as a weighted average of the maturities of the individual payments

™It is an important measure for investors to consider, as bonds with higher durations carry more risk and have higher price volatility than bonds with lower durations

Duration is also a point where the investor faces no interest rate risk

Macaulay DurationThe formula usually used to calculate a bond’s basic duration is the Macaulay duration

 

n = number of cash flows t = time to maturity

C = cash flow

r = required yield (YTM)

M = maturity (par) value

Simplified Equation:

Derivatives for CFP –   1

Forwards

A forward contract or simply a forward is a contract between two parties to buy or sell an asset at a certain future date for a certain price that is pre-decided on the date of the contract. Features of Forwards:

1. The price fixed now for future exchange is the forward price.2. The party with a “long position”(“Short position) will be the buyer(seller) of the

underlying asset or commodity.

3. Custom tailored

4. Traded over the counter (not on exchanges)

5. No money changes hands until maturity

6. Counter-party risk

Settlement of Forward Contracts:1. Physical Settlement2. Cash Settlement

Futures

Like a forward contract, a futures contract is an agreement between two parties in which the buyer agrees to buy an underlying asset from the seller, at a future date at a price that is agreed upon today. However, unlike a forward contract, a futures contract is not a private transaction but gets traded on a recognized stock exchange. Futures contract is standardized by the exchange. 

Features:

1. Standardized contracts in terms of:o Underlying commodity or asset

o Quantity

o Maturity, delivery date and delivery terms

2. Exchange traded

3. Guaranteed by the clearing house — no counter-party risk

4. Gains/losses settled daily

5. Margin account required as collateral to cover losses

 Margins:

Initial Margin: The payment which investors have to pay to a broker to trade on margin, commonly used in trading futures and contracts for difference. Initial margin is usually set at a percentage of the value of the contracts being traded.Maintenance Margin: The lowest balance of funds that a broker will allow a counterparty to maintain when trading on margin.Variation Margin: Profits and losses on open futures contracts, which are revalued daily at the settlement price, which are subsequently paid to or received from the clearing house. Basis:The difference between the current cash price and future price is defined as basis.

Basis = Current cash price – Futures price

Negative basis refers to Contango market where futures prices are higher than cash prices. Positive basis refers to backwardation market where futures prices are lesser than cash prices. 

Derivatives for CFP –   2

Posted by Prashant Shah on December 15, 2011

Relevance of futures market:

Quick and low cost transactions Price discovery function (fair idea of future demand and supply)

Advantage to informed individuals (Impart efficiency to the price)

Hedging advantage

 Futures trading

Advantages Disadvantages 1. Leverage : Smaller cash outlay i.e. Only margin amount

1. Risk : Trading loss more than initialinvestment

2. Ease of Short Selling: It is possible to sell futures without possessing the underlying

2. No stockholder privileges : No voting rights and no rights to dividends

3. Flexibility : Can use the instrument to speculate, hedge, spread or othersophisticated strategies

3. Required vigilance : Require investor to monitor their position because of marked to margin and margin call

Payoff for a buyer of Nifty futures:

The investor bought futures when the index was at 2220. If the index goes up, his futures position starts making profit. If the index falls, his futures position starts showing losses.

Example and Picture Source: NCFM Books, www.nseindia.com

Payoff for a seller of Nifty futures:

The investor sold futures when the index was at 2220. If the index goes down, his futures position starts making profit. If the index rises, his futures position starts showing losses.

Introduction to Equity   Investment

Posted by Prashant Shah on February 17, 2011

What is Equity?

In simplest words we can say that equity means ownership. An equity share is commonly referred to as ordinary share and it represents the form of fractional ownership in which a shareholder is a fractional owner where they undertakes the maximum entrepreneurial risk associated with a business or a company.

Types of shares:

Apart from the ordinary share of a company, shares can be further classified into

Rights Shares: Rights shares are the shares which are offered to the existing share holders normally at a price which is lower than the current market price of the shares. One of the prime reason for the rights issue is to reduce the cost of raising money to the company. Bonus Shares: These are the shares which are offered to the existing shareholders without any cost. Theoretically bonus issue should not change wealth of the shareholder of the company because when the shares are received there should be relevant decline in the share prices. Some of the reasons for bonus issue are to capitalize the reserves of the company, to bring share price once again in reach of the normal investors and to act as anti takeover measure in certain cases.Preferred Stock/ Preference shares: These are the shares which are paid fixed dividend. They have a preference over  ordinary shareholders in claiming dividend from the profit of the company. They are different from ordinary shares because they don’t carry voting right and they are redeemable. Cumulative Preference Shares: If the company doesn’t have adequate profit in a particular year the claim of preferred holders are carried forward to next year. Hence these are cumulative preference shares. Cumulative Convertible Preference Shares: These are the preference shares which are converted in to ordinary shares of the company at the time of maturity Warrants: Warrant are normally attached with the debt instruments. The holder of the warrant has a long-term right to buy ordinary shares at fixed price on the fixed future date. Warrants are normally issued with the debt instruments to lure investors. The investors in the equity market can be classified as follows:Investor: He is the person who invests in a company with long-term investment objective. He wants to profit from the growth of the company. His risk and returns are proportionate. Speculator: He is the person who loves to bet on the prices of the share. His investment horizon is short. The level of risk which he assumes and the returns which he gets is not proportionate. Arbitrager: They are mainly involved in the market to make risk free profits. They buy from one market and sell in other market as and when price discrepancy arises.

Valuation of Equity Shares: Dividend Discount Model   (CFP)

Posted by Prashant Shah on September 2, 2011

Value  is what we perceive and price is what we pay. Valuation is the process to know the worth of the thing for which we pay a price. It a process through which we can refine our investment decision and it also serves a base to buy an asset.

Valuation means present value of all the future benefits Financial theory says that the value of a stock is worth all of the future cash flows

expected to be generated by the firm, discounted by an appropriate risk-adjusted rate

According to the DDM, dividends are the cash flows that are returned to the shareholder

Zero Growth Model

This model assumes that there will be no growth in the dividend paid by the company and the company will pay the same dividend every year. This means that there is a 100% Dividend payout ratio and no retention of dividends.

Valuation:

Constant Growth Rate Model (Gordon Model)

A model for determining the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate. This model assumes the constant growth rate over the long term.

Valuation:

 Limitations:

Applicable to those firms which pay dividend Applicable only to those firms that are growing at a steady growth rate

If the growth rate is equal to the required rate of return the price of the stock approaches to infinity

Commercial Paper   (CP)

Commercial paper performs the financial disintermediation function. CP is a short-term instrument, introduced in 1990, to enable non-banking companies namely Corporates, Financial Institutions (FIs), Primary Dealers (PDs) to borrow short-term funds through liquid money market instruments. CPs were intended to be part of the working capital finance for corporates. Features of CP:

1. CP can be issued either in the form of a usance promissory note or in a dematerialized form through any of the depositories approved by and registered with SEBI.

2. Issued subject to minimum of Rs 5 Lakh (face value) and in the multiples of Rs. 5 Lakh thereafter,

3. Maturity is 7 days to 1 year

4. Unsecured and backed by credit of the issuing company

5. CP may be issued on a single date or in parts on different dates provided that in the latter case, each CP shall have the same maturity date.

Who can invest in CP?

1. Individuals,2. Banking companies,

3. Other corporate bodies registered or incorporated in India

4. Non-Resident Indians and Foreign Institutional Investors (However, investment by FIIs would be within the limits set for their investments by SEBI).

Factors affecting price of CP:

1. Call money market rates2. Competing money market investment products

3. Liquidity

4. Credit rating

Calculations are same as we did for treasury bill as CPs are also issued at discount to face value.

Who is eligible to issue CP:

A corporate would be eligible to issue CP provided –

1. the tangible net worth of the company, as per the latest audited balance sheet, is not less than Rs. 4 crore

2. company has been sanctioned working capital limit by bank/s or all-India financial institution/s; and

3. the borrowal account of the company is classified as a Standard Asset by the financing bank/s/ institution/s.

The minimum required credit rating for CP is P2 by CRISIL or equivalent if rated by other rating agency.

Repurchase Agreements/Repo   Agreements

Posted by Prashant Shah on May 3, 2011

Whenever the banks have any shortage of funds they can borrow it from RBI. Repo rate is the rate at which our banks borrow rupees from RBI. A reduction in the repo rate will help banks to get money at a cheaper rate. When the repo rate increases borrowing from RBI becomes more expensive.

Leg-1

Leg-2

[A Repo deal is one where eligible parties enter into a contract with another to borrow money against at a pre-determined rate against the collateral of eligible security for a specified period of time. The legal title of the security does change. The motive of the deal is to fund a position. Though the mechanics essentially remain the same and the contract virtually remains the same, in case of a reverse Repo deal the underlying motive of the deal is to meet the security / instrument specific needs or to lend the money. Indian Repo Market is governed by Reserve Bank of India. At present Repo is permitted between permitted 64 players against Central & State Government Securities (including T-Bills) only at Mumbai. Source: www.fimmda.org]

Normally for the repo and reverse repo auctions amount is periodically published by the RBI and the targets are mainly given to the primary dealers. When the RBI feels that there is excess liquidity in the system, it will focus more on reverse repos and vice versa.

Repo transactions can be made for a period which commences with an overnight and maximum period is 14 days. However overnight repos are popular. When repo rate increases, it clearly gives signals of increase in the overall rates of interest. Both are rates are also known as the policy rates and are extremely useful weapons to the regulator.

Risk and Return for   CFP-5

Posted by Prashant Shah on March 19, 2013

Modern Portfolio Theory and Asset Pricing

The relation between portfolio returns and portfolio risk was recognized by two Nobel Laureates in Economics, Harry Markowitz and William Sharpe. Harry Markowitz tuned us into the idea that investors hold portfolios of assets and therefore their concern is focused upon the portfolio return and the portfolio risk, not on the return and risk of individual assets.

The relevant risk to an investor is the portfolio’s risk, not the risk of an individual asset. If an investor considers buying an additional asset or selling an asset from the portfolio, what must be considered is how this change will affect the risk of the portfolio.

Possible Portfolio

 The Efficient Frontier: the best combinations of expected return and standard deviation.

All the assets in each portfolio, even on the frontier, have some risk. Now let’s see what happens when we add an asset with no risk—referred to as the risk-free asset.

If we look at all possible combinations of portfolios along the efficient frontier and the risk-free asset, we see that the best portfolios are no longer those along the entire length of the efficient frontier; rather, the best portfolios are now the combinations of the risk-free asset and one and only one portfolio of risky assets on the frontier.

Sharpe demonstrates that this one and only one portfolio of risky assets is the market portfolio—a portfolio that consists of all assets, with the weights of these assets being the ratio of their market value to the total market value of all assets.

If investors are all risk averse—they only take on risk if there is adequate compensation—and if they are free to invest in the risky assets as well as the risk-free asset, the best deals lie along the line that is tangent to the efficient frontier. This line is referred to as the capital market line (CML). If the portfolios along the capital market line are the best deals and are available to all investors, it follows that the returns of these risky assets will be priced to compensate investors for the risk they bear relative to that of the market portfolio.

The CML specifies the returns an investor can expect for a given level of risk. The CAPM uses this relationship between expected return and risk to describe how assets are priced.

The CAPM specifies that the return on any asset is a function of the return on a risk-free asset plus a risk premium. The return on the riskfree asset is compensation for the time value of money. The risk premium is the compensation for bearing risk. Putting these components of return together, the CAPM says:

Expected return on an asset = Expected return on a risk-free asset + Risk premium

Hence, Required rate or return = Rf + (Rm – Rf) β

Where,  (Rm – Rf) is Market Risk Premium

For each asset there is a beta. If we represent the expected return on each asset and its beta as a point on a graph and connect all the points, the result is the security market line (SML) 

Security Market Line:

Risk and Return for   CFP-6

Posted by Prashant Shah on March 25, 2013

Risk Adjusted Performance Measurement (Important for Examination)

The Sharpe measure

Sharpe (1966) defined this ratio as the reward-to-variability ratio, but it was soon called the Sharpe ratio in articles that mentioned it. It is defined by

This ratio measures the excess return, or risk premium, of a portfolio compared with the risk-free rate, compared, this time, with the total risk of the portfolio, measured by its standard deviation.

If the portfolio is well diversified, then its Sharpe ratio will be close to that of the market. With this ratio the manager can check whether the expected return on the portfolio is sufficient to compensate for the additional share of total risk that he is taking. Since this measure is based on the total risk, it enables the relative performance of portfolios that are not very diversified to be evaluated, because the unsystematic risk taken by the manager is included in this measure.

The Treynor measure

The Treynor (1965) ratio is defined by

The term on the left is the Treynor ratio for the portfolio, and the term on the right can be seen as the Treynor ratio for the market portfolio, since the beta of the market portfolio is 1 by definition. Comparing the Treynor ratio for the portfolio with the Treynor ratio for the market portfolio enables us to check whether the portfolio risk is sufficiently rewarded.

The Treynor ratio is particularly appropriate for appreciating the performance of a well diversified portfolio, since it only takes the systematic risk of the portfolio into account.

The Jensen measure

Jensen’s alpha (Jensen, 1968) is defined as the differential between the return on the portfolio in excess of the risk-free rate and the return explained by the market model, or

Illustration:

You are evaluating the rankings based on Sharpe and Treynor Ratio of three funds A, B and C . The average returns obtained from funds A, B and C have been 16%, 19% and 14%, respectively against the market return of 13%. The standard deviations of fund returns have been 17, 22 and 16, respectively versus the market return standard deviation of 15. If the beta reported of these funds is 1.2, 1.4 and 1.1, respectively and the risk-free rate of return is 5.5%, what are your rankings in the order of best to worst?