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Futures on equity indices

Alternative methods of weighting

It is generally considered that capitalization weighted indices give the most accurat indication of the collective movement in corporate asset or liability prices. However two alternative methods of weighting the constituents of equity indices are fowl,equally weighted‘ and ‘price weighted‘. In the case of equally weighted indices, a’ equal amount of money is assumed to be invested in each security in the index Changes in the index thus represent changes in the value of the portfolio. Pri weighted indices reflect the average price of the securities in the index and Chang: in the index represent the average price change of the securities in the index. The Dow—Jones and the Major Market Index of the American Stock Exchange (MMI) a. both of the price weighted form. The FT 30 is a geometric average equally weight index. Only the Major Market Index has a futures contract based upon it. Read more »

Valuing American options on futures contracts

The Black model should not be used for valuing American options on currency futures because it may be optimal to exercise the options early in the same way as it may be optimal to exercise options on the spot currency early. The binomial or the Barone-Adesi and Whaley models may be used for valuing those options.

The early exercise potential of American options on futures is different to that of options on the spot. Futures prices do not exhibit the discrete jumps that accompany spot market assets when the underlying spot asset makes discrete distributions. However, as the carry basis of the future converges to zero at delivery, the futures price converges to the spot price in an orderly manner. Read more »

Average rate options

Average rate currency options are based upon the average exchange rate of the underlying currency as distinct from the exchange rate on a single date — the expiry date.

The advantage of an average rate option is that the volatility of a moving average of a variable is less than the volatility of individual observations of that same variable. With daily observations, and with the volatility levels seen in the currency markets, the volatility of the moving average is in the order of 60% of that of the raw observations. Consequently, the price of an average rate option with a given exercise price will be less than an otherwise identical standard European currency option. Read more »

Empirical evidence of the term structure continue…

Term structure based option-pricing models

Term structure models of pricing contingent claims have followed one of two approaches. One approach followed by Cox, Ingersoll and Ross (1985) actually model the expected returns from movements in the term structure in order to price the contingent claims. In effect, the term structure becomes endogenous to the pricing of the contingent claim.

The second approach followed by Ho and Lee (1986), Heath, Jarrow and Morton (1989), Black, Derman and Toy (1990) and Hull and White (1990) utilizes the volatilities of the various sectors of the term structure to derive a probability distribution of an arbitrage-free binomial, trinomial or multinomial lattice of the term structure. From this lattice, contingent claims are priced. These models all have one thing in common: they allow for the whole-term structure to be stochastic instead of the price of a single underlying instrument or a single interest rate. The whole-term structure is represented at each node of the binomial, trinomial or even multinomiaf lattice. Read more »

The debt instruments with embedded options continue…

Bonds with equity warrants attached

Recently it has been popular among Japanese corporations to issue eurobonds with equity warrants attached. Their popularity has stemmed partly from the strength of the Tokyo stock market, the warrants giving an equity kicker to bond investors.

These warrants are usually detached from the bonds after issue, and traded separately. Bonds with warrants attached are different from convertible bonds because the warrants are long-term options which when exercised require new cash, not existing bonds, to be exchanged for the new equity. At the time of issue, the bonds constitute a portfolio consisting of one bond and one long-term option on the equity of the issuer. After the time of issue, and when the warrants have been stripped, the bonds are valued as straight bonds. Read more »

Where Do You Look for the Next Paul Tudor Jones? Part 3

The professionals within this industry have their own trade association, the Managed Futures Association. Its function is to assist members, to promote the industry, and to advance the industry. They produce an excellent monthly professional journal that discusses issues important to members, everything from legislation, regulatory compliance, trade execution, to marketing. Their annual membership directory is an excellent source to find CTAs and CPOs.

Commodity pool operators are the individuals or corporations who structure funds. These are pools of commingled money from a number of individual investors. Most of the funds are large enough to require multiple CTAs. If the funds are properly selected, this further reduces risk, as we saw earlier. Most CPOs closely follow the performance of a large number of CTAs and analyze their performance. For this reason, CPOs can be excellent consultants in CTA selection. Read more »

International Investing Concerns and Limitations Part 1

There are a variety of concerns with international investing and limitations of the analysis cited in previous sections. These limitations are discussed below and may weaken the case for international investing.

Increasing and Varying Correlations

Concern

The key benefit from international investing arises because of low correlations between the domestic market and foreign markets. There are two criticisms of historical correlations. First, the correlations may be increasing due to greater global integration as evidenced by larger capital and trade flows. Moreover, as more and more emerging markets liberalize capital flows, the correlations will increase. If the correlations are increasing, the above analysis based on prior data overestimates the benefit from international investing. Reconsider the example in the preamble of “Evidence,” above. With a correlation of 0.60, the new portfolio’s risk fell from 18 percent to 16 percent. However, if the correlation is 0.70 instead of 0′:60, then the new portfolio’s risk falls less, from 18 percent to 16.6 percent. If the correlation is 0.8, then the risk is 17.1 percent.

You can see that the gains from international investing can quickly erode with an increase in correlations. Read more »

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