Stocks - I

Common stocks are also called equity securities. They represent an ownership interest in the company and entitle the owner of the stocks to the share of the cash flows of the company, which is generally referred to as dividends. In case of liquidation, the pro-rata share of the company valuation is shared with the owners.

Preferred stock is another kind of ownership in form of stocks. They are different from the common stocks as they have fixed dividend payments irrespective of the earnings of the company, and are received before any payment is made to the common stock holders. Thus they receive fixed dividend and are senior to the common stocks.

In the United States, secondary market trading in common stocks has occurred in two different ways. The first is on organized exchanges, which are specific geographical locations called trading floors, where representatives of buyers and sellers physically meet. The trading mechanism on exchanges is the auction system, which results from the presence of many competing buyers and sellers assembled in one place.

The second type is via over-the-counter (OTC) trading, which results from geographically dispersed traders or market-makers linked to one another via telecommunication systems. That is, there is no trading floor. This trading mechanism is a negotiated system whereby individual buyers negotiate with individual sellers.

The electronic exchange market has developed in nearly all the countries and allows for instant trade over the communication medium. This medium of trading resembles more of the organised exchange system sans the trading floor.

The markets are categorised as first, second, third and fourth, where the first market refers to the trading on exchanges of stocks listed on an exchange; second market refers to the trading in the OTC market of stocks not listed on an exchange; third market refers to the trading on the OTC market of stocks listed on an exchange; and fourth market refers to the private transaction between institutional investors dealing directly without any intermediary.

Listed stocks are those which are listed on an exchange.

Members are those people who have the right to trade shares on the exchange.

Dually listed stocks allow trading of stocks on more than a single exchange.

A commission broker is an employee of a securities house (“stockbrokers” or “wirehouses”) devoted to handling business on the exchange. Commission brokers execute orders for their firm on behalf of their customers at agreed commission rates. These houses may deal for their own account as well as on behalf of their clients.

Independent floor brokers work on the exchange floor and execute orders for other exchange members who have more orders than they can handle alone or who require assistance in carrying out large orders. Floor brokers take a share in the commission received by the firm they are assisting. Registered traders are individual members who buy and sell for their own account. Alternatively, they may be trustees who maintain membership for the convenience of dealing and to save fees.

Specialists are dealers or market makers assigned by the stock exchange to conduct the auction process and to maintain an orderly market in one or more designated stocks. Specialists may act as both a broker (agent) and a dealer (principal).

Advantages provided by an exchange

Exchange helps in the following:

• Price discovery
• Provides diversity of participants
• Increased availability of capital to the listed companies
• Increase exposure for the company
• Increased accountability of the all the management personnel of the company
• Increased liquidity for the investors

Types of orders

• Market order – order to be fulfilled at the best price available in the market. Here the buyer giving the highest price is given a priority over the lower prices
• Public order – the order which is given be member for investors other than its own firm. This order is given priority over the order given by the members for their own firm.
• Limit order – this has a price threshold designated
• A buy limit order means that the stock is to be purchased only at the given price or lower
• A sell limit order means that the stock is to be sold only at the given price or higher
• Stop order – this order is not to be executed until the market moves to a designated price after which it becomes a market order
• A buy stop order means that the order is not to be executed until the market reaches (rises to) a designated price
• A sell stop order means that the order is not to be executed until the market reaches (falls below) a designated price
• A stop-limit order, a hybrid of a stop order and a limit order, is a stop order that designates a price limit. In contrast to the stop order, which becomes a market order if the stop is reached, the stop-limit order becomes a limit order if the stop is reached. The stop-limit order can be used to cushion the market impact of a stop order. The investor may limit the possible execution price after the activation of the stop. As with a limit order, the limit price may never be reached after the order is activated, which therefore defeats one purpose of the stop order—to protect a profit or limit a loss.
• Market if touched order - This order becomes a market order if a designated price is reached. A market if touched order to buy becomes a market order if the market falls to a given price, while a stop order to buy becomes a market order if the market rises to a given price. Similarly, a market if touched order to sell becomes a market order if the market rises to a specified price, while the stop order to sell becomes a market order if the market falls to a given price. We can think of the stop order as an order designed to get out of an existing position at an acceptable price (without specifying the exact price), and the market if touched order as an order designed to get into a position at an acceptable price (also without specifying the exact price).
• Fill or kill order – this order needs to be executed as soon as it reaches the trading floor or is cancelled
• Open order (good till cancelled) – this order continues to be in existence until it is cancelled specifically
• Round lot – generally consists of 100 shares
• Odd lot – consists of shares less than the round lot
• Block trade – it consists of 10,000 shares or is of value more than US $0.2 million

Investment Returns

Any form of investment has an objective of increasing the amount of money or value of the asset which the investor has invested. Return is the parameter which can be used to measure the performance of the financial asset and is also helpful in evaluation of the asset. Return is generally which attracts the investors towards a financial asset over others, assuming all other conditions to be same.

A rate of return is the gain received from an investment over a period of time expressed as a percentage. Though the returns for a simple investor can be easy and require only unitary skills, the formulas can turn to be complex for the following reason:

• Selection of proper inputs to calculate return
• Treatment of additional client contributions and withdrawals to and from the investment account
• Adjusting the return to reflect the timing of these contributions and withdrawals
• Differentiating between the return produced by the investment manager and the return experienced by the investor
• Computing the returns spanning multiple valuation periods
• Averaging periodic rates of return

Single Period Rate of Return

The rate of return concentrates a lot of information into a single statistic. Individual data points about the beginning and ending market values, income earned, cash contributions and withdrawals, and trades for all of the holdings in the portfolio are compressed into a single number. It is faster for an investor to analyse proportions than absolute numbers. Returns are comparable even if the underlying figures are not. Returns calculated for different periods are comparable; that is, an investor can compare this year’s return to last year’s. Return is the value reconciling the beginning investment value to the ending value over the time period we are measuring.

MVE = MVB * (1 + Decimal Return)

MVE = market value at the end of the period

MVB = market value at the beginning of the period

Return in per cent = (gain or loss) / (investment made) * 100

Generally the returns are calculated ignoring the time value of money whereby the investment made is assumed to have been made only prior to the sale of the asset. The rate of return can be rewritten as,

(gain or loss)/(investment made)*100 = ((current value/investment made)–1)*100

The equation leads to,

(MVE – MVB)/MVE, or, (MVE/MVB – MVB/MVB), or, (MVE/MVB – 1)

The numerator is the unrealised gain or loss; in fact it should be given as market value plus the accrued income. The denominator is always the investment made or the money which is put to risk.

For instance, the investor invests on 1 January, Rs. 100, and it rises to Rs. 110 at the end of January and then to Rs. 120 at the end of February. The gains are thus calculated as:

1 – January: 100

1 – February: 110 return = (110-100)/100 = 10%

1 – March: 120     return = (120-110)/110 = 9.09%

This procedure where the market value of the investment has been used to calculate, the gain on the investment has been recognised, though it is not actually realised as there has been no sale done. For calculating returns which include the unrealised gain, the returns are measured at the end of each measurement period, the dates of which are called valuation dates. A return between two valuation dates is known as a single period, holding period, or periodic return.

To sum up, when there are no transactions into and out of an investment account and no income is earned the ending value is simply divided with the beginning value. In case of portfolio, the total market value is derived by summing up the individual asset value in the portfolio.

The unit value is simply calculated by dividing this value with the total number of shares outstanding. This is done using a methodology called trade date accounting. Here the securities are included in the portfolio valuation on the day the manager agrees to buy or sell the securities, as opposed to waiting for the day the trades settle with the broker.

The market value of each security is the amount we would expect to receive if the investment were sold on valuation date. There are a number of factors like liquidity, estimating the exact current value and future cash flows which make this process hard.

The individual security market value include a measure of income earned or accrued income. This is the income which the investor has earned but is yet to receive. For example, in bonds, there are generally semi-annual coupons, thus between the time of coupon payments, the investor has earned the interest, though that would be received only on the coupon date. Returns which include both the change in the market value and the income earned is called the total return. Similar adjustments are made when considering the portfolio as a unit.

Thus the single period return calculation formula can be written as:

[((ending market value + ending accrued income)/(beginning market value + beginning accrued income)) – 1] * 100

Here the cost of investment has not been included in the calculation. Also for each subsequent period, the ending market value for the previous period is used as the beginning value for the next period. Here it is assumed that for each valuation period the amount of money invested is the unrealised gain and not the initial investment made.

Return on investment

The previous section gave information about the single period return calculation. In real life scenarios, the investors make additional investments and also withdraw from the portfolio. In case of contributions/withdrawals the calculation for the gain/loss is:

Gain/loss = (current value – original investment – net cash inflows + net cash outflows)

If the above cash flows are adjusted into the formula for the return, the result is the return on investment.

ROI in percent = ((EMV+NOF)-(BMV+NIF))/(BMV+NIF) * 100

In all the above formulas the timing of the cash flow and also the duration for which the investment has been made is not considered.

Time value of money

To project the future value of money, the formula used is

FV = PV * (1 + R)^N

Here the present amount of money is multiplied with the interest rate applicable. This is possible because of the fact that interest rates are known whereas the returns are not. Thus the future value of an investment is equal to the present value plus the interest and other gains earned over the period.

Compounding is the reinvestment of income to earn more income in subsequent periods. Here the implicit assumption is that any cash flow is reinvested at the same rate of interest and thus the future value is calculated. As it can be seen from simple calculations the power of compounding makes the returns to be large in nature. As time passes, the total returns increase more than what the simple interest would have given and also the interest-on-interest increases. Interest-on-interest is the interest which is earned on an initial interest which has now been assumed to have been reinvested at the same rate of interest.

Interest rates are quoted in annual basis and the same can be adjusted for lesser time period compounding:

MVE=MVB*(1+rate of interest/compounding frequency)^{(periods * compounding frequency)}

When the numerator and the denominator values are adjusted for the time, and the contributions and withdrawals are taken as such that the time component have been added using the time value of money formula, the denominator is known as the average capital employed or the average interest balance.

Performance of an investment: money-weighted returns

Timing of investor decision

Market timing is the term which relates the time an investor makes his investment to the market cycle. Based upon the time the investor invests or sells the investment return can vary.

The concept can be explained with a simple example. The period and the return table can be redrawn as:

Period	Market Value	Return
1	100	-
2	120	20%
3	110	-8.33%
4	115	4.55%

As seen in the table, the returns for the periods are given in the third column. Had the investor invested in period 1 and sold the investment in period 2, the return is 20% whereas, if the investment had been sold in period 4, neglecting the time value of money, the return would have been only 15%. These decisions of investing and selling the investment are dependent upon the investor and not on the manager.

Timing of investment manager decision

The investment of the amount of cash at disposal of the manager would depend on the manager herself.

Take for example, that the first manager decides to keep a portion of the cash aside and not invest it and the second manager using same amount of money decides to invest the whole of the fund in the market. Now, if the market moves up, and the market returns are more than the returns which are earned on the non-invested money (can be assumed to be nominal in nature), the second manager stands to gain more than the first and vice-versa.

Segregating investor and manager timing decision

As it can be seen from the above discussion, if the investor and the manager are two different persons then the responsibility of the decisions would be dependent upon them. Thus there is a need to segregate the investor and the manager timing decisions. The decisions are:

·        The timing of investor decisions to make an investment into the portfolio

·        The decisions made by the manager to allocate assets and select securities within the portfolio

The money weighted return (MWR) is used when we need to measure the performance as experienced by the investor. MWR is a performance statistic reflecting how much money was earned during the measurement period. This amount is influenced by the timing of decisions to contribute or withdraw money from a portfolio, as well as the decisions made by the manager of the portfolio. The timing and size of the cash flows have an impact on the ending market value:

Transaction	Before Market	Effect on Performance
Contribute	Goes Up	Positive
Contribute	Goes Down	Negative
Withdraw	Goes Up	Negative
Withdraw	Goes Down	Positive

Though the above data can be used to segregate the cash flows, in order to account for the timing of the cash flows, they have to be discounted for the appropriate amount of time.

Take for example, that the investments are made at the start of each period.

Time Period	Months Invested	Period Weight
0	12	1.00
1	11	0.92
2	10	0.83
3	09	0.75

As shown in the table, the cash flows for different time periods can be adjusted using the period weights.

MWR is found by calculating the IRR (Internal Rate of Return) for all the cash flows and changing the time parameter to reflect the true value for individual cash flows. The formula for the calculation of the IRR is given as:

MVE = MVB (1+IRR) + CF₁ (1+IRR) + CF₂ (1+IRR)² +….+ CF_n (1+IRR)ⁿ

The values for the MVE and MVB and the different cash flows are required to calculate the IRR.

As IRR calculation is dependent upon the trial and error, it can be tedious to calculate. To minimise the time and calculate the rate of return approximately, the Modified Dietz Return (MDR) formula was devised.

MDR = (MVE-MVB-CF)/(MVB+((CD-C_i)/CD)*CF_i) * 100, where

CF = net amount of cash flows for the period

CD = total days in the period

C_i = the day of the cash flow

CF_i = the amount of the net cash flow on C_i

Performance of the investment manager – time-weighted returns

Time-weighted return (TWR) is the statistics that completely eliminate the impact of investor cash flows. The time weighted return (TWR) is a form of total return that measures the performance of a dollar invested in the fund over the complete measurement period. The TWR eliminates the timing effect that external portfolio cash flows have on performance, leaving only the effects of the market and manager decisions.

The steps to calculate the TWR are:

1. Begin with the market value at the beginning of the period.
2. Move forward through time toward the end of the period.
3. Note the value of the portfolio immediately before a cash flow into or out of the portfolio.
4. Calculate a subperiod return for the period between the valuation dates.
5. Repeat 3 and 4 for each cash flow encountered.
6. When there are no more cash flows, calculate a subperiod return for the last period using the end of period market value.
7. Compound the subperiod returns by taking the product of (1 + the subperiod returns).

The last step is called the chain linking or geometric linking, which is similar to compounding.

TWR = [(1+R₁) * (1+R₂) * …. * (1-R_n) – 1] * 100, where,

R_n are sub-period returns.

Sub-period return is calculated using the formula MVE/(MVB + NCF).

Multiple-period return calculation

Cumulative return is the rate of return which the investor receives due to the growth rates for the different sub-periods.

CR = [GR1*GR2*….*GRn – 1]*100

Arithmetic mean return is the arithmetic average of the returns for the different sub-periods. The formula for the same is:

AMR = (Sum (periodic returns))/(count of returns)

Geometric mean return is the n-th root of the product of the returns of the different sub-periods.

GMR = [ⁿ√ (1 + cumulative return) – 1] * 100

Annualising returns less than a year – the geometric mean return when calculated for a 1-year period is called an average annual return, compound annual return, or annualised return. The formula for the same is given as:

{[(1 + period rate)^{# of periods}] – 1} * 100

Annualising returns greater than a year – the formula is:

{[(# of years√ (1 + period rate)] – 1} * 100

AR = [(number of days / 365.25 √linked growth rates) – 1] * 100, where,

 

linked growth rate = (1+R₁) * (1+R₂) …. (1+R_N)

Compound annual internal rate of return – this can be calculated from the general formula of the compound annual rate of growth where the periods are divided into multiples of a year.