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  • #31
    2. Calendar spreads

    The principle of operation of calendar spreads is somewhat different from vertical spreads. The investor does not use the difference in prices for various options, but the time factor, that is, the time value of the options. We know that the longer the time until the expiration of an option, the more time value is invested in the price of that option. It is this feature that is used when creating a calendar spread: an investor buys an option with a certain expiration date in the future (say, two months) and simultaneously sells an option with the same strike, but with a shorter expiration period (for example, one month).

    The psychology of this option strategy is based on the fact that the time value of the option tends to zero as the expiration date approaches. The investor believes that in the near future the asset price will remain unchanged, or will change only slightly. It is for this purpose that he sells a nearby option, and buys a more distant option as a hedge of risk:

    Calendar spread


    XYZ Stock: $ 80
    June Call 85: 1
    July Call 85: 1 ½
    Content of the strategy Position value
    Buying July Call 85 and Selling June Call 85(-1 ½ x 100) + (1 x 100)
    (Calendar Call Spread)= - $ 50

    Note: Investor believes that the price of XYZ shares will not be able to rise above $ 85 until the expiration date in June, so he will be able to earn from the premium he will receive from the sale of the June Call option. However, please note that after the expiration of the first Call option, the investor will have a “long” position in the form of the July Call option. What does this mean? The fact that the investor in the longer term is quite positive, that is, "bullish" outlook on shares of XYZ and he hopes that by July the shares of this company will rise above $ 85, that is, he will be able to make money on his "long" July Call -option.


    XYZ Stock: $ 80
    June Put 75: 1
    July Call 75: 1 ½
    Content of the strategy Position value
    Buying July Put 85 and Selling June Put 85(-1 ½ x 100) + (1 x 100)
    (Calendar Put Spread)= - $ 50

    Note: This calendar spread using Put options is very similar to the previous one, with one exception. The investor, as in the case of the Call calendar spread, believes that in the next month the share price will not change much and he will be able to make money on the fall in the term value of the option that he sold. The difference is that in a month the investor will have a “long” Put option in his hands, that is, he has a “bearish” view of the prospects for XYZ shares. He hopes that in July the shares will fall in price and he will be able to make money on a “long” Put option.


    • #32
      3. Diagonal spreads

      Diagonal spreads are a combination of vertical and calendar spreads. The "long" and "short" options in the diagonal spread not only have different strikes, as in the vertical spread, but also have different expiration dates, as in the diagonal spread. The general psychology of a diagonal spread is analogous to the psychology of a normal vertical spread. However, there are nuances that predetermine the choice of a diagonal spread rather than a vertical one: the investor notices that the cost of short-term options is overstated compared to the usual situation. A similar situation is possible against the backdrop of intense rumors that suddenly emerge around the XYZ stock. For example, a merger or takeover of a company is expected, or the release of some very important, sometimes even sensational, statements. In such a situation, the premiums of short-term options increase sharply (for Call options - in case of positive expectations from the upcoming news, or in Put options - in case of negative expectations).


      XYZ Stock: $ 100
      March Call 100: 4
      May Call 100: 5
      March Call 105: 3
      May Call 105: 4
      Content of the strategy Position value
      Buying May Call 100 and Selling March Call 105(-5 x 100) + (3 x 100)
      (Diagonal Spread)= - $ 200

      The investor in this case took advantage of the relatively overpriced nearby options and sold them. In addition to this, he set a vertical spread because he is short on a high strike option and a “long” position on an option with a lower strike.

      When talking about diagonal spreads, we used an interesting phrase: "the price of an option is overstated compared to the usual situation." When is it safe to say that the price is overpriced or underpriced? Another question - overpriced in relation to what? And what is a common situation?

      The fact is that there are purely mathematical, or rather, statistical methods for assessing the so-called "theoretical" value of options. This theoretical cost is considered to be normal or fair for a particular option. To determine this theoretical value, rather complex statistical calculations are used, which are called "option pricing models". There are several such models, but the most famous are the Binomial Cox-Ross-Rubinstein Model and the Black-Scholes Model. It is believed that the binomial model is more accurate, but in the vast majority of cases, the simpler Black-Scholes model is used, since the degree of its accuracy is more than satisfactory for the individual investor.


      • #33
        4. Proportional spreads

        The last group of spreads is proportional spreads. The main difference between proportional spreads and the vertical, diagonal and calendar spreads we have already considered is that we buy one number of options and sell a different amount. Let's look at the main proportional spreads:

        Proportional spread using Call options (Call Ratio Spread) - with this strategy, the investor buys Call options with a lower strike and sells more Call options with a higher strike:

        Proportional Call Spread


        XYZ Stock: $ 100
        March Call 100: 4
        March Call 105: 2
        Content of the strategy Position value
        Buy 2 March Calls 100 and sell 2 March Calls 1052 (-4 x 100) + 2 (2 x 100)
        (Bull Call Spread)= - $ 400

        Buy 2 March Calls 100 and sell 4 March Calls 1052 (-4 x 100) + 4 (2 x 100)
        (Call Ratio Spread)= 0

        The psychology of this strategy is similar to the usual vertical bullish spread, but there are a number of fundamental differences. Firstly, the expectation of growth in shares is an order of magnitude lower than with the usual vertical “bullish” spread. The graph shows that the investor receives the maximum profit if by the expiration date the shares have grown only slightly and preferably have not exceeded the upper strike. At the same time, the owner of the vertical spread gets the maximum profit even if the share price has exceeded the upper strike. This relative inconvenience is more than offset by the almost complete absence of costs (with the exception of commissions and temporary collateral for short options) to create a position by selling more Call Options with an upper strike.

        Proportional spread using Put-options (Put Ratio Spread) - this strategy requires a bearish view of the state of the asset, but to a much lesser extent than in the case of the traditional bearish vertical spread. The investor buys Put options with a higher strike and sells more Put options with a lower strike:

        Proportional Put Spread


        XYZ Stock: $ 100
        March Put 100: 4
        March Put 95: 2
        Content of the strategy Position value
        Buy 2 March Puts 100 and sell 2 March Puts 952 (-4 x 100) + 2 (2 x 100)
        (Bear Put Spread)= - $ 400

        Buy 2 March Puts 100 and sell 4 March Puts 952 (-4 x 100) + 4 (2 x 100)
        (Put Ratio Spread)= 0

        Everything that has been said above about the psychology of Call Ratio Spread fully applies to Put Ratio Spread, but with the opposite sign - instead of bullish expectations, the investor has a restrained bearish outlook.

        Reverse spread using Call options (Call Backspread) - with this strategy, the investor buys more Call options with a higher strike and sells fewer Call options with a lower strike:

        Reverse Call Spread


        XYZ Stock: $ 103
        March Call 100: 5
        March Call 105: 2
        Content of the strategy Position value
        Sell ​​2 March Calls 100 and buy 3 March Calls 1052 (5 x 100) + 3 (-2 x 100)
        (Call Backspread)= $ 400

        Obviously, Call Backspread is an extremely bullish strategy. On the chart, we see that the investor is interested in the maximum growth of the shares, in any case, the upper strike (105) must be broken through without fail. Please note that we have a credit spread, so the investor will be fine if the stock falls below the lower strike on the expiration day. In this case, both "long" and "short" options will be "out of the money" and will lose any value, but the investor will earn $ 400, which he received at the very beginning, when setting the position.

        Reverse spread using Put options (Put Backspread) - with this strategy, the investor buys more Put options with a lower strike and sells fewer Put options with a higher strike:

        Reverse Put Spread


        XYZ Stock: $ 100
        March Put 100: 3
        March Put 105: 6
        Content of the strategy Position value
        Sell ​​2 March Puts 105 and buy 3 March Puts 1002 (6 x 100) + 3 (-3 x 100)
        (Put Backspread)= $ 300

        The psychology of this strategy: the investor is interested in a strong fall in the stock price. In this case, his profit is practically unlimited. However, he will be satisfied with a situation in which the share price will rise sharply, then both "short" and "long" options expire in vain, and the investor will keep the received $ 300 loan.

        We have completed a painful exploration of options and various option strategies. Now is the time to talk about something simple, for example, securities with options features.


        • #34
          Derivative securities. Futures. Securities with options features.
          Some financial instruments are very similar to options, although they are not. Let's consider them briefly:

          1. Warrants - options (put or call), written by the firm itself on its own shares. The purpose of warrants is to either make the acquisition of shares in a company more attractive or to reward employees. Warrants differ from options in the following ways:

          - Warrants have a long lifespan (five years or more) or are generally unlimited.

          - At the time of the initial issue, warrants are “out of the money”, that is, the strike price is higher than the current market value of shares for call warrants, or lower for put warrants.

          - A warrant grants the right to buy (or sell) only one share (and not one hundred, as with ordinary options).

          - Warrants are protected from share split and dividend payments.

          - The number of issued warrants is always fixed and limited (that is, it does not depend on supply and demand, as is the case with ordinary options).

          2. Rights (rights) - derivative securities, in many respects similar to warrants. The purpose of the rights is to provide shareholders with an advantage when purchasing ordinary shares of a new issue even before their public offering. Rights, like warrants, are issued on a per share basis. Unlike warrants, rights have a very short life span - from two to ten weeks from the date of issue. All this time, the old shares are sold "with rights" (cum rights), that is, by purchasing such shares, the investor also receives the rights to a new issue. After some time, the shares decrease in price and are sold “without rights” (ex-rights). Finally, the last difference between rights and warrants is that the rights strike is usually in the money.

          3. Convertible securities - a financial instrument that can be converted into another asset of the same issuer. The most common convertible securities are bonds and preferred shares, which can be converted into common stock. The conversion is done using the conversion ratio. Let's say the conversion rate is 100. This means that one convertible bond can be exchanged for 100 common shares. Typically, the conversion rate at the time a convertible bond is issued makes it unprofitable to immediately exchange it for shares - until the share price rises to a certain value. In this respect, convertible bonds are similar to warrants, which have a “out of the money” strike at the time of issue.

          Now let's talk about the most speculative securities - futures contracts. If anywhere you can get rich literally "overnight", it is on the futures markets.


          • #35
            Futures contracts
            A futures contract is a contract for the delivery of an asset on a specified date in the future at a specified price.

            At the time of entering into a futures contract, the buyer does not pay and the seller does not deliver the goods. Instead, both the buyer and the seller post a certain deposit, which serves as a guarantee against the refusal of any of the parties to fulfill their obligations. Since the market value of an asset changes on a daily basis, the amount of the collateral is also reviewed daily (either decreases or increases).

            An asset of futures contracts (FC) can be:

            - agricultural products: livestock, cocoa, coffee, corn, cotton, pork, orange juice, soybeans and butter, sugar, wheat, etc.;
            - natural resources: copper, crude oil, gasoline, gold, kerosene, timber, platinum, silver, etc .;
            - foreign currency: British pound, Canadian dollar, German mark, Japanese yen, Swiss franc;
            - fixed income securities: eurodollar bonds, municipal bonds, treasury bills, tickets and bonds;
            - market indices: Nikkei, S&P 500, E-Mini S&P 500, S&P Midcap 400, MMI (Major Market Index), GSCI (Goldman Sachs Commodity Index), Russell 2000, S&P 500 / BARRA Growth, S&P 500 / BARRA Value, Nasdaq 100, IPC.


            • #36
              FC trades on the following exchanges:

              1.CBOT (Chicago Board of Trade)
              2. CME (Chicago Mercantile Exchange)
              3. COMEX (New York Mercantile Exchange - COMEX)
              4. CSCE (Coffee, Sugar, and Cocoa Exchange)
              5. KCBT (Kansas City Board of Trade)
              6. MGE (Minneapolis Grain Exchange)
              7. MIDAM (MidAmerica Commodity Exchange)
              8. NYCE (New York Cotton Exchange)
              9. NYFE (New York Futures Exchange)
              10. NYMEX (New York Mercantile Exchange)


              • #37
                The FC price is indicated in basis points. Each FC has its own contract size. The cost of FC is determined by the formula:
                FC cost = Price x Contract size


                The price of FC on the S&P 500 index is 950 points. The size of the FC is $ 250. Then the cost of one FC per S&P 500 index is 950 x 500 = 237,500 dollars.
                There are two types of futures contracts:

                - speculation - operations with FC, the purpose of which is to buy at a cheaper price and sell at a higher price (it is not necessary in this sequence, and vice versa - first sell at a higher price and then buy at a lower price);

                - hedging (hedge) - these operations are carried out by the owners of the asset (called a spot) to eliminate the risk.

                Buying a FC is called a “long position”.
                Selling a FC is called a “short position”.

                Examples of speculation:

                The trader believes that the OA market will go up. He buys FC on the S&P 500 at a time when the price is 950 points.

                The market index is growing and the value of FC rises along with it. When its price reaches, say, 960 points, the investor will close his “long” position, that is, sell a similar FC. This procedure is called a reversing trade. As a result, he will receive a profit (excluding commissions): (960-950) x250 = 2500 dollars.

                Hedging example:

                The corn producer notes that in one of the winter months the price of July FC for corn is 295 points, which is quite satisfactory for him. Suppose he does not want to take risks if the price drops sharply in six months and he has to sell the crop at a low price. Therefore, he opens a “short” position, that is, he sells the July FC already in the winter and, thus, “freezes” (lock-in) profits in the winter.

                The peculiarity of FC is that they are not concluded directly between the buyer and the seller. There is always an intermediary between them - the clearinghouse. Therefore, the whole scheme of the FC transaction looks like this:

                1. The buyer promises to pay the cost of the FC to the clearinghouse.
                2. The clearing house promises to pay the cost of the FC to the seller.
                3. The seller promises to deliver the asset to the FC clearinghouse.
                4. The clearing house promises to deliver the asset under the FC to the buyer.

                Thus, the clearinghouse serves not only to regulate the FC market, but also acts as a guarantor for both the seller and the buyer.

                At the very beginning, it was said that in order to open "long" or "short" positions, the trader does not need to pay the cost of the entire FC. Both the buyer (long) and seller (short) must post an initial performance bond. Typically, the amount of the initial collateral is only 2-10% of the total cost of the FC. This allows you to get phenomenal leverage when trading FC.


                The trader placed a long position in FC on the S&P 500 at 950 points. The amount of the initial collateral for this FC is currently 12,563 dollars, which is the size of the initial investment. At the end of the day, the FC price was set at 962 points, and the trader made a reverse trade:

                (962 - 950) x250 = $ 3,000.

                So an initial investment of $ 12,563 yielded $ 3,000, which is 24% in one day.


                • #38
                  Accounting for a futures account is carried out as follows. Every day after the end of the trading session, a recalculation takes place in order to reflect the changes that have occurred during the day. This recalculation is called clearing (marking to market). As a result of daily clearing, the trader's futures account consists of two amounts: the initial margin and the sum of all daily wins minus daily losses.

                  The main requirement for maintaining a futures account is that the balance must not be less than 65% of the initial margin. If the balance is less than this value, the trader is obliged to deposit additional funds and bring the account to the initial margin. These additional funds are called variation margin. If the trader does not make the variation margin, his broker closes the position using a reverse trade, even if this procedure turns out to be unprofitable for the trader.


                  The movement of funds in the futures account of a trader speculating on the FC on the S&P 500 index (the size of the initial collateral is $ 12,563, the variation margin is $ 10,050):

                  DayFC Price Action Amount Total
                  1,950 Opening a "long" position 12563 12563
                  2 965 Clearing +3750 16313
                  3,961 Clearing -1000 15313
                  4,944 Clearing -4250 11063
                  5 950 Clearing +1 500 12563
                  6,930 Clearing, variation margin 7,563 12,563
                  7 940 Clearing +2500 15063
                  8,960 Clearing, reverse trade -20063 20063
                  So, the trader invested $ 17563 (12563 + 5000) within 8 days. As a result, he received $ 20063. The profit is $ 2,500, or 14%.

                  Obviously, the huge "leverage" provided by the FC can lead to very serious consequences if the market suddenly moves sharply in a direction unfavorable for the investor. In order to reduce the risks from possible non-payments, daily limits are set on the futures exchanges, which restrict the movement of futures prices. These limits are different for FC. There are also such FCs for which daily limits are not set.


                  • #39
                    Futures Arbitrage
                    An important action is associated with FC. We are talking about the so-called futures arbitrage, which interferes with the natural course of events on the stock exchange every day.

                    Futures arbitrage is the simultaneous buying and selling of a FC and its spot.

                    OA markets are primarily influenced by arbitrage, which is carried out on futures contracts on the S&P 500 index and common stocks included in this index.

                    For any arbitrage situation to arise, it is necessary that the same asset in different places costs differently. Therefore, the question immediately arises: how does the price of an index futures contract compare with the index itself? Obviously, the price of an index futures is closely tied to the index itself. When you buy an index futures, you are, in effect, acquiring the right to a block of shares included in the index. If there was an opportunity to buy an index futures, say, at half the price of the index itself, then no one would have worked for a long time. Everyone would only do what they buy a cheap index and immediately sell (short) expensive stocks included in this index.

                    Thus, we can draw the first conclusion that the price of a futures can deviate from the value of the index only by a small distance. As soon as this deviation exceeds a certain value, an arbitrage situation arises, that is, the possibility of simultaneously buying and selling a FC and its asset in order to realize an instant guaranteed profit.

                    What is this "certain value"? It is called the fair value of the futures contract.

                    For mathematically educated readers, here is the formula by which the fair value of a futures contract is calculated:

                    FV = SPX * (1 + r) t - Div
                    FV - fair value of a futures contract;
                    SPX - the value of the S&P 500 index;
                    r - interest rate on treasury bills (T-Bills);
                    t is the lifetime of the futures contract (in years);

                    Div is the sum of all dividends that are paid on shares included in the S&P 500 index during the life of a futures contract.


                    The value of the S&P 500 index is 945.22 points.
                    Until the expiration of the nearest futures contract - 83 days (0.2274 years)
                    T-Bills yield - 5.44%
                    The sum of all dividends is $ 7.41.
                    Then the fair value will be:

                    FV = 945.22x (1 + 0.0544) x0.2274-7.41 = 945.22x1.0121-7.41 = 949.2648

                    Often the FV value is indicated not in absolute terms, but in the form of a premium (premium) or a discount in relation to the index itself:

                    945.22-949.26 = 4.04

                    In our example, the fair value of an S&P 500 futures contract is a premium of 4.04 points.

                    The fair value of a futures contract, in fact, reflects the cost of maintaining a basket of stocks included in the index. These costs are called cost-of-carry (COC). In our example, the additional 4.04 points will be the cost of maintaining all the stocks included in the S&P 500 index for the entire period until the FC expires.


                    • #40
                      Suppose the nearest futures contract is valued at 949.26 points, that is, equal to fair value.

                      Let's try to play arbitrage: we buy shares at their current value (-945.22) and at the same time sell FC (+949.26). It seems that we have guaranteed ourselves a profit of 4.04 points. In fact, if you subtract the cost of maintaining these shares, which is exactly 4.04 points, our arbitrage will not bring any profit.

                      In reality, FC, like any security, fluctuates depending on supply and demand. At some point, demand may far exceed supply, and the futures price will rise above its FV. Or vice versa - it will fall below FV if there are more sellers than buyers. This is when the real situation for index arbitrage will arise! Moreover, this happens several times a day.

                      Suppose, due to increased demand, the price of FC was 955 points. The “arbitrageur” immediately notices that the price of the futures is much higher than its fair value, which means that a real arbitrage situation has been created. So, the "arbitrageur":

                      1. Buys a basket of S&P 500 stocks at -945.22 points.

                      2. Sells "expensive" futures at +955 points.

                      At the same time, the "arbitrageur" ​​remembers that in fact, he should add the fair value of the basket to the purchase price:

                      - (945.22 + 4.04) +955 = + 5.74

                      This is the profit from futures arbitrage on each contract. Naturally, you should deduct from it the costs of commissions, which, however, are very small for professional "arbitrageurs".

                      In reality, the profit from the described arbitration situation will be lower. The fact is that the massive sale of FC in a matter of seconds leads to a drop in its price. At the same time, massive buying of shares will lead to an instant rise in the S&P 500 itself. As a result, the arbitrage situation will last for a very short time. Therefore, the "arbitrageur" ​​will never get down to work if the difference between the cost of the FC and its fair value does not reach a certain value, which guarantees that under any circumstances it will still be possible to get some profit.

                      This value depends on a number of subjective factors, for example, on the efficiency of access to the trading terminal of this or that "arbitrageur". The faster his car, the smaller the gap between the fair value and the price of the futures can be. On average, it is believed that successful arbitrage requires futures to be at least 0.70-0.90 points above fair value. This value is called the buy program.

                      Naturally, index arbitrage can be carried out in the other direction. Suppose that the price of the futures has dropped below fair value, that is, a "discount" has arisen. In this case, the arbitrageur does the opposite: he buys cheap futures and actively sells shares. The amount of gap between the fair value and the futures price required to initiate discount arbitrage is called the sell program.

                      Massive selling programs triggered by discount futures arbitrage lead to a violent dumping of stocks and a sharp drop in their quotations. Buying programs, on the other hand, cause the market to skyrocket.

                      Arbitration situations, due to the gigantic size of the capital involved in them, are visible to the naked eye on any chart. Here is a typical example - we have before us a day in the life of the Dow Jones Industrial index.


                      • #41
                        Market indices.
                        Types of accounts and orders.
                        How to evaluate the behavior of not a single stock, but a whole group (for example, the banking or engineering sector) or the entire market as a whole? Market indices are used to assess the global processes taking place in the securities markets.

                        5. Market indices

                        Based on the results of day trading, one can immediately answer the question of how this or that security behaved today - whether it rose or fell in price, or remained unchanged.
                        The market index is an indicator of the behavior of a group of securities, or of the entire market as a whole.
                        The market index is usually calculated using a statistical weighting procedure. Four types of weighing are used:

                        1. Weighting of stock prices (price weighting).
                        2. Value weighting.
                        3. Equal weighting.
                        4. Weighing the geometric mean (geometric eighting).

                        Let's move in order.

                        5.1. Weighing stock prices

                        Suppose we need to calculate an index that includes three securities - A, B and C. On the first day of calculation (day 0), shares A, B and C had prices:

                        A - 10 dollars
                        B - $ 20
                        C - $ 30

                        The price-weighting index is calculated using the following formula:

                        (S1 + S2 ... + Sn) / d,

                        where S1 is the price of the first share,

                        S2 - the price of the second share,
                        Sn - the price of the last share included in the index,
                        d - divisor.

                        If stocks were not split from time to time (you remember that stock splits are one of the forms of dividend payments), then the divisor would always be equal to the number of securities included in the index. Since a stock split results in a price change, the divisor must be adjusted each time.

                        So, on day 0, our index will be:
                        (10 + 20 + 30) / 3 = 20

                        Now suppose that the next day (day 1) stock A was split 1: 2 and C stock was split 1: 3. The closing prices on the second day were:

                        A - 6 dollars
                        B - $ 21
                        C - $ 11

                        If we did not change the divisor, then the value of the index could be calculated using a more complex formula:

                        ((6x2) +21+ (11x3)) / 3 = 22

                        However, if the index is calculated over a long time and includes a large number of stocks, then after several splits the calculation will turn into unbearable agony. Therefore, it will be more practical to calculate the new divisor. Basically, you need to solve the equation:

                        (6 + 21 + 11) / d = 22,

                        whence we obtain d = 1.7273. So, the new divisor after two share splittings will not be 3, but 1.7273.

                        Let's calculate our index for one more day (day 2). There were no more splits, and the prices were as follows:

                        A - 7 dollars
                        B - $ 20
                        C - 10 dollars
                        Our index on day 2 is:

                        (7 + 20 + 10) / 1.7273 = 21.42

                        Note: Usually on the first day, the index is counted not from zero, but from some given level, for example 100. Then the value of the index on day 0, day 1 and day 2 will be:

                        Day 0 - 120
                        Day 1 - 122
                        Day 2 - 121.42

                        This is how the market index is calculated based on the weighting of stock prices. The most famous of this type are the Dow Jones indexes, developed by Charles Dow, founder of the Dow Jones. There are three Dow Jones indices:

                        • Dow Jones Industrial Average. It includes 30 companies from the industrial sector. This is the index that you see every day in newspaper headlines and television news bulletins;
                        • The Dow Jones Transportation Average tracks the behavior of 20 transport companies and
                        • Dow Jones Utilities Average based on 15 utility companies.

                        The popularity of the Dow Jones indices is primarily due to tradition. The fact is that price weighting, which is the basis of the Dow indices, is not the best option, since it does not take into account the number of shares of a particular company included in the index. As a result, there is an unjustified bias towards “expensive” shares, regardless of the level of the firm's capitalization.

                        The company capitalization is taken into account in the so-called indices, based on weighing the value of securities, not their price.


                        • #42
                          5.2. Value weighting

                          Let's go back to our example. Suppose that the following number of shares of companies A, B and C are circulating on the open market:

                          A - 100,000 shares
                          B - 200,000 shares
                          C - 300,000 shares.

                          Their initial capitalization will be:

                          A - 100,000x $ 10 = 1,000,000 dollars
                          B - 200,000x $ 20 = 4,000,000 dollars
                          C - 300,000x $ 30 = 9,000,000 dollars

                          The calculation of the index based on weighting the value of the shares is done as follows:

                          1. The total capitalization on day 0 is calculated:
                          (100,000x $ 10) + (200,000x $ 20) + (300,000x $ 30) = 14,000,000 dollars;

                          2. The value of the index on day 0 is taken as a conventional value, for example, 100;
                          3. The total capitalization on day 1 is calculated taking into account the splitting:
                          (200,000x $ 6) + (200,000x $ 21) + (900,000x $ 11) = 15,300,000 dollars

                          4. The capitalization on day 1 is divided by the capitalization on day 0 and multiplied by the value of the index on day 0, that is, by 100:
                          ($ 15,300,000 / $ 14,000,000) х100 = 109.29 - this is the value of the index on day 1.

                          5. The procedure is repeated for all subsequent days. So, for day 2:
                          (200,000x $ 7) + (200,000x $ 20) + (900,000x $ 10) = 14,400,000 dollars
                          ($ 14,400,000 / $ 14,000,000) х100 = 102.86

                          The summary table of our index will look like this:

                          Day 0______100
                          Day 1 ______ 109.29
                          Day 2 ______ 102.86

                          Most modern market indices are based on weighting the value of stocks. The most famous index of this type is Standard & Poor's 500, which includes the five hundred largest (capitalized) companies on the American market. Standard & Poor's 500 includes 400 industrial companies, 40 utility companies, 40 financial companies, and 20 transportation companies.

                          Other market indices based on value weighting:

                          • The Nasdaq Composite records about 5,000 OTC stocks;
                          • NYSE Composite covers almost all stocks traded on the New York Stock Exchange (about 2300 companies);
                          • Russell 2000 and 1000 is an index tracked by the Frank Russell Company (Tacoma, WA). Russell 1000 includes 1000 of America's most highly capitalized companies. Russell 2000 targets so-called small cap companies, small cap companies. This definition includes firms with a capitalization of less than $ 380 million (a funny figure for the Russian market!).
                          • Wilshire 5000 is the most voluminous market index, tracking 5000 companies traded on NYSE, AMEX and Nasdaq.

                          For computer professionals, indices that measure technology sector securities are of particular importance. As an example, I will cite the group of technology indices of the Goldman Sachs company (Goldman Sachs Technology Indexes, GSTI), which are also based on cost weighting:

                          • GSTI Hardware Index (symbol - GHA) - manufacturers of computer equipment;
                          • GSTI Internet Index (GIN) - Internet-oriented companies;
                          • GSTI Multimedia Networking Index (GIP) - multimedia and network companies;
                          • GSTI Semiconductor Index (GSM) - semiconductor companies;
                          • GSTI Software Index (GSO) - software companies;
                          • GSTI Services Index (GCV) - computer services companies.


                          • #43
                            5.3. Weighing arithmetic and geometric mean values ​​(equal and geometric weighting).

                            These two types of market indices stand apart. They are prepared by Value Line. The first index is called the Value Line Composite (Arithmetic) Index, the second is the Value Line Composite (Geometric) Index.

                            Value Line Indices track the stocks of over 1,700 companies. Their calculation is based on the principle of investing the same amount of money in different securities. Obviously, more cheap shares can be purchased for the same amount. For this reason, the Value Line Index is more sensitive to fluctuations in cheap rather than relatively expensive securities.

                            The arithmetic index is calculated using the following algorithm:

                            1. First, the relative change in the price of each share in comparison with the previous day is calculated:
                            On day 1, taking into account crushing:

                            A - (6x2) / 10 = 1.2
                            B - 21/20 = 1.05
                            C - (11x3) / 30 = 1.10

                            2. The arithmetic mean of the relative changes is calculated:
                            (1.2 + 1.05 + 1.10) / 3 = 1.1167

                            3. The conditional value of the index on day 0 (for example, 100) is multiplied by the resulting arithmetic mean:
                            100x1.1167 = 111.67 - the value of the index per day 1

                            4. The procedure is repeated on all subsequent days:

                            On day 2:
                            A - 7/6 = 1.1667
                            B - 20/21 = 0.9524
                            C - 10/11 = 0.9091
                            (1.1667 + 0.9524 + 0.9091) / 3 = 1.0094
                            111.67 (index value on the previous day) х1.0094 = 112.72 - index value on day 2

                            Index summary table:

                            Day 0_______100
                            Day 1_______ 111.67
                            Day 2 _______ 112.72

                            The algorithm for calculating the geometric index is similar to the arithmetic one, however, instead of the arithmetic mean value, the geometric mean value is taken. The geometric mean of relative price changes is calculated using the formula:
                            (S1 x S2 ... x Sn) 1 / n,
                            where S1 is the relative change in the price of the first share,
                            S2 is the relative change in the price of the second share,
                            Sn - the relative change in the price of the last stock,

                            In our example:

                            1. The geometric mean of the relative changes on day 1 is calculated:
                            (1.2x1.05x1.10) 1/3 = 1.1149

                            2. Index value per day 1:
                            100x1.1149 = 111.49

                            3. Calculation of the index on day 2:
                            (1.1667x0.9524x0.9091) 1/3 = 1.0034

                            111.49 (index value on the previous day) х1.0034 = 111.87

                            Index summary table:

                            Day 0 _______100
                            Day 1 _______ 111.49
                            Day 2 _______ 111.87

                            We see that all indices react to the rise and fall of stocks, however, they differ greatly both in absolute and in percentage terms. Notice how the indices reacted to the price changes that occurred on day 2. The price-value-weighting indices fell that day, while the Value Line indices, on the contrary, recorded a rise. Why? The decisive factor was the 17% rise in the price of the relatively cheap A stock (from $ 6 to $ 7). Remember that in the Value Line indices, “cheap” stocks play a very important role.

                            What practical conclusion can we draw from this observation? Only one - the art of trading, first of all, is based on the ability to take into account the most varied factors of market behavior. Therefore, it is very useful to track not only the Dow Jones index, but also the rest. In this case, it is especially important to take into account the specifics of each index, namely, the principle of weighting, which underlies its calculation.


                            • #44
                              6. Types of accounts and orders

                              I have already said that an ordinary investor can participate in securities trading through a brokerage office. To do this, you need to open a brokerage account in one of them. Choosing a broker, signing an agreement with him, the initial amount required to open an account - we will consider all these issues at the beginning of the second - practical - part of our course. Now we will get acquainted with such purely theoretical aspects of the problem as the types of brokerage accounts, as well as the types of orders for the purchase and sale of securities.


                              • #45
                                6.1. Types of brokerage accounts

                                The first type of account is cash (cash account). The peculiarity of a cash account is that in order to purchase securities, you must pay their full value. In other words, you cannot use any credit provided by the brokerage company. However, this does not mean that at the time of purchase of securities, 100% of the market value of the purchased securities should be in your cash account. The fact is that all transactions must be settled within three business days. This period is called the settlement period. It is during this period that you must fully pay for the purchase. In turn, the broker must credit the purchased securities to your account no later than the last day of the settlement period, which is called the settlement day.

                                It should be remembered that the three-day billing period is set only for common stocks, bonds and treasury bills. The settlement period for options is one day, and at the time of purchase, your account must have the funds necessary to pay 100% of the options cost.

                                If you fail to fulfill your obligations during the settlement period, you risk your broker liquidating the position and freezing the account for a long period (usually 90 days) as a punishment. If the position is liquidated at a loss, you will have to pay for that too.

                                If your account is frozen, you still have access to it, but you can only buy securities if there are sufficient funds on the account at the time of placing a trade order to pay their full value.

                                There is one more subtlety associated with the billing period, which must be constantly borne in mind. Let's say you bought 100 shares of company XYZ at $ 100. As a rule, you have three days to place the payment for this purchase in your brokerage account. However, the next day, the stock rallied and you sold it for $ 105. As a result, you made a profit of $ 500. However, you still need to deposit money for the original purchase within three days, otherwise you will be in breach of your obligations.

                                The second type of account is a "margin account". A margin account allows you to pay only a partial value of the purchased securities. The missing funds are lent to you by a brokerage firm. The amount of margin has changed throughout history and, from 1974 to the present, according to the rules of the Federal Reserve Board, is 50%. That is, in order to purchase securities, you need to have half of the current market value of these securities in your margin account. Basically, a margin account is a kind of leverage because your purchasing power doubles. Accordingly, every dollar invested can bring double the returns compared to a regular cash account. The risk of buying on margin is that the potential losses are doubled.

                                Obviously, you will have to pay interest to the brokerage office for the loan provided. Interest is calculated daily and added to the principal amount of the debt (the so-called multiplication).
                                Interest rates vary among brokerage firms, but usually do not exceed 2 percent above the centralized broker call loans.
                                Debit balance - the amount borrowed from a brokerage firm to buy using margin.
                                Initial margin - the minimum starting capital required for margin operations, which is 50% of the value of the purchased securities.

                                The account margin is recalculated on a daily basis and is adjusted depending on changes in the market value of securities. This recalculation is called marking to the market.

                                Consider this example:
                                Y stock price - $ 60
                                You purchase 100 shares of Y into your margin account. The initial position looks like this:
                                Market value of shares $ 6,000

                                • Debit balance $ 3,000 (50%)
                                • Margin (equity) $ 3000 (50%)

                                The next day, the stock price drops to $ 58. The new position is:
                                Market value of shares $ 5,800

                                • Debit balance $ 3,000 (52%)
                                • $ 2800 margin (48%)

                                Suppose that after some time, as a result of the further fall of shares of Y, their price was 40 dollars. Position calculation:
                                Market value of shares $ 4,000

                                • Debit balance $ 3,000 (75%)
                                • $ 1,000 margin (25%)