Value characteristics of securities
The indicator of the development of the securities market is their profitability, and the initial basis for determining the yield of bonds, certificates and other securities - their price.
The price of bonds can be nominal (nominal), redemption and market.
The nominal price is printed on the bonds (issue price). It serves as a base for calculating interest and further recalculating prices.
Redemption price - the price at which the issuer buys a bond. It can coincide or not coincide with the nominal price and depends on the terms of the loan.
Market ( exchange rate ) price is formed in the securities market and depends on demand and supply on it.
Government bonds are characterized by a periodic payment of income in the form of interest. Payment is made on coupons - cut-out coupons with coupon rates indicated on them.
The interest rate can be of several kinds.
1. Fixed rate - exactly set by size; it is usually applied in the absence of inflation.
2. Floating Rate. Floating rate bonds are issued in the conditions of inflation, depreciation of money and loss of interest by creditors to bonds with a solid interest. In order to take into account the rate of inflation, the state starts issuing bonds with floating interest rates (floating coupon). In this case, the size of interest on bonds depends on the level of loan interest.
3. Step interest rate. The interest rate change is differentiated by loan years. The above method of setting the interest rate can be combined with the indexation of the nominal (exchange rate) value of bonds (increasing it as inflation increases).
4. Zero coupon and mini coupon (interest-free and low-interest bonds). When bonds with a bullet coupon are issued, the emission rate is set lower than the nominal value by the discount amount. Bonds with a mini-coupon are a transitional type to a zero coupon. Coupon yield is lower than usual, but the discount from the issue price is also less than for zero-coupon bonds.
Calculation of bond yields. When determining the yield of a bond, first of all you should find its initial base - nominal (nominal) price P and :
where З - loan amount; К - number of issued bonds.
The price of the initial placement of bonds, or the issue price, sometimes does not coincide with the nominal price. As a result, there are two options:
- the issue price is less than the nominal price; such a price is called a discount, or a discounted price ;
- the issue price is more than the nominal, i.e. The security is placed with a premium.
When the sale of the debt obligation in the secondary market there is a market price, the rate of which is the ratio of the market price (Pp) to the nominal price liabilities (PH):
where Кц - price rate.
Buying a bond or a certificate, an investor buys them at an issue or exchange price, and they are repaid, as a rule, at a nominal price. Depending on loan conditions, these prices may not coincide. The difference between the redemption price and the purchase price of a security characterizes the increase or loss of capital for the entire loan period.
If a bond is redeemed at par, and it was bought at a discount (Rd), then the investor eventually has a capital gain.
Yield of the bond in this case is higher than that indicated on the coupon.
If a bond is bought at a price with a premium (Pn), then upon the redemption of this paper, its owner suffers a loss.
In this case, the yield of a bond purchased with a premium is lower than the price indicated on the coupon. The bond can be purchased at a nominal price, then the yield of the bond is equal to the coupon yield.
The listed bond yield options allow you to calculate annual growth rates or loss of capital.
where Дг - absolute size of a gain or loss of the capital for a year; D - the absolute amount of capital gain or its loss for the entire loan period; t - number of loan years.
The annual additional yield ( I e), or the rate of additional income, is determined by the formula
where Дпр - the purchase price of the bond.
Yield of the bond is determined by two values: coupon payments (reward for the loan given to the issuer) and the difference between the repayment price and the bond purchase price.
Coupon payments are made annually (sometimes once a quarter or half a year); they are expressed in percentages or in absolute values.
The absolute value of the annual return (Ar) is determined by the formula
where I is the annual coupon rate,%.
The coupon current yield is calculated by the formula
The coupon yield depends largely on the loan term (here the link is inverse: the longer the maturity of the bond, the higher the yield percentage), the quality of the security and, above all, its reliability.
To determine the profitability of securities, formulas of ordinary and exact interest are widely used. They are applied, in particular, in cases where the bond is not sold at the beginning of the fiscal year and coupon payments must be divided between the previous owner and the new one.
When calculating simple interest assume that each month of the year contains 30 days, and a year - 360 days. In this case, coupon payments are due to the bond seller:
where - the coefficient of ordinary interest (Kob);
P is the number of calendar days from the last & quot; percentage & quot; day before the day of bond redemption. & quot; Interest & quot; day is the date of the coupon payment.
Coupon payments based on exact percentages can be determined by the formula
where - the coefficient of exact percentages (CD.
Applying these formulas, you can determine both components of bond yields: coupon payments and the difference between the redemption price and the purchase price of the bond. As a result, the annual aggregate income and total income for the entire loan period will be calculated.
The size of annual total income is equal to the amount of coupon payments and the annual increase (or loss) of capital (DG):
where Dk is the coupon yield for the entire loan period.
Hence the annual aggregate return, or the cumulative yield rate, is
where P pr - purchase price of the bond.
Total income for the entire loan period can be determined by summing up coupon payments for all years and capital gain (loss) for the entire loan period:
where Dk - coupon income for the entire loan period; DKAP - increase (loss) of capital for the entire loan period; I to - the coupon annual rate; Рн - nominal price of the bond.
Total income for the entire loan period can be determined differently, based on the amount of annual aggregate income:
where P is the number of years of the loan.
When working with securities, it is important to know the incremental cost. It can be determined if you add coupon payments to the redemption price for the entire loan term:
where С - the increased cost; P and - the redemption price (nominal price); I to - coupon rate; P is the number of years of the loan.
You can also calculate the period through which the accrued value will reach a certain value or size of the coupon rate:
Calculation of stock returns. The return on a share depends on the size of the dividend (part of the corporate profit distributed), the opportunity to sell the paper in the secondary market at a price higher than the purchase price.
Dividend is the portion of the distributed profit of a corporation (joint stock company) per share. It can be expressed in monetary units or in the form of an interest rate. Interest rate is determined by dividing the absolute amount of dividend income by the nominal share price:
where i д - dividend rate; I e - dividend income.
The current return on a stock is determined by rendit, or the current income rate:
where R - rents the stock; P pr - the purchase price of the share (issue or market).
Rendit allows you to determine how many monetary units of income the shareholder has received for each invested monetary unit.
If the stock is sold in the middle of the fiscal year, the dividend amount should be divided between the former and the new owners. In this calculation, you can use the formula of either ordinary or exact percentages.
by the formula of ordinary percentages
by the formula of exact percentages
where Dob is the buyer's income using the ordinary interest formula; Дт - the income of the buyer under the formula of exact percent; I г - the annual size of the dividend; t - the number of days from the date of acquisition of the share until the date of the next dividend payment.
In addition to the dividend, the source of income may be the difference between the purchase price and the sale price if the stock price increases. Additional income (loss) in the sale of shares can be determined in absolute monetary units and percentages.
Absolute value of additional income (loss) equals the difference between the exchange price (the sale price) of the share and the purchase price:
where Dd - additional income; P to - the stock price of the stock (sale price).
Additional income in percent can be calculated by dividing the absolute value of the additional income by the purchase price of the share (issue or market):
Having determined the dividend and the additional income, you can find the aggregate or final income:
Hence the cumulative or final, the return in percent (the rate of aggregate income) is equal to
The above formulas for determining the yield of stocks and bonds allow not only to calculate the income from the securities available to the investor, but also to use them in the formation of the securities portfolio, the choice of its best structure (diversification), as investments in securities not only bring income, but also associated with a certain risk. When developing an investment strategy and tactics, a rich international experience can be used to apply various methods for estimating the future value of investments. Fundamental and technical analysis is widely used to select the most effective and reliable areas for investing in stock instruments in world practice. studying the state of the economy and the stock market in general, as well as evaluating the potential of various securities through a number of listed qualitative indicators.
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