Issuing bonds at discount - computing effective interest rate
In this case the market interest rate is the discount rate that sets equal the market price (current value) of the bond to its present value. To find the market interest rate which is also referred to as promised yield YTM you would have solve for the interest rate in the bond price formula A market price of bond is the sum of discounted coupons and the terminal value of the bond. Most spreadsheet programs and calculators have a RATE function that makes possible finding this market interest rate. First see this for finding a coupon paying bond price The coupon payments are discounted so is the par value of the bond and sum of such discounts is the market price of the bond. The TVM functions in Excel and calculators make this possible using the following equation Let us take your data, 9% $100,000 coupon with 5 years remaining to maturity with market interest rate of 10%. Bonds issued in the US mostly pay two coupons per year. Thus we are finding the present value of 10 coupons each worth $4500 and par value of $100,000. The semi-annual market interest rate is 10%/2 or 5% The negative sign indicate money going out of hand Now solving for RATE is only possible using numerical methods and the RATE function is programmed using Newton-Raphson method to find one of the roots of the bond price equation. This rate will be the periodic rate in this case semi-annual rate which you have to multiply by 2 to get the annual rate. Do remember there is a difference between annual nominal rate and an annualized effective rate. To find the market interest rate  If you don't have Excel or a financial calculator then you may opt to use my version of these financial functions in this JavaScript library tadJS "Yes, the ""effective"" and ""market"" rates are interchangeable. The present value formula will help make it possible to determine the effective interest rate. Since the bond's par value, duration, and par interest rate is known, the coupon payment can be extracted. Now, knowing the price the bond sold in the market, the duration, and the coupon payment, the effective market interest rate can be extracted.  This involves solving large polynomials. A less accurate way of determining the interest rate is using a yield shorthand. To extract the market interest rate with good precision and acceptable accuracy, the annual coupon derived can be divided by the market price of the bond." If the market rate and coupon were equal, the bond would be valued at face value, by definition. (Not 100% true, but this is an exercise, and that would be tangent to this discussion).  Since the market rate is higher than the coupon rate, the value I am willing to pay drops a bit, so my return is the same as the market rate.  This can be done by hand, a time value of money calculation for each payment. Discount by the years till received at the market rate to get the present value for each payment, and sum up the numbers.  The other way is to use a finance calculator and solve for rate.  The final payment of $10,000 (ignore final coupon just now) is $10,000/(1.1^5). In other words, that single chunk of cash is worth 10% less if it's one year away, (1.1)^2 if 2 years away, etc.  Draw a timetable with each payment and divide by 1.1 for each year it's away from present. If the 9% coupon is really 4.5% twice a year, it's $450 in 6 month intervals, and each 6 mo interval is really 5% you discount.  Short durations like this can be done by hand, a 30 year bond with twice a year payments is a pain.  Welcome to Money.SE.
"There's actually a lot of smaller questions in your question, so I'll answer just a few here. The standard bond index for high yield corporates is the Barclays Capital High Yield Corporate index, which is the basis for JNK.  I am not familiar with the index behind HYG, the ""iBoxx $ Liquid High Yield index."" The ETFs are managed quantitatively to try to track the index as closely as possible.  AFAIK these ETFs do not attempt to take active positions. New issues are typically purchased with cash which is constantly coming in from interest and principal payments from other bonds.  There is rarely a need to sell bonds just to buy new issues.  Selling bonds is more common when a fund is experiencing redemptions. These ETFs and the high yield bonds they buy are not derivatives (your question seems to be confused on that point). The US Treasury is not directly involved in any way.  They are indirectly involved, as they are indirectly involved in US equities markets or world markets for that matter, although perhaps they have greater influence in the bond world. Moody's has extensive studies of default rates by ratings." "The fundamental concept of the time value of money is that money now is worth more than the same amount of money later, because of what you can do with money between now and later. If I gave you a choice between $1000 right now and $1000 in six months, if you had any sense whatsoever you would ask for the money now. That's because, in the six months, you could use the thousand dollars in ways that would improve your net worth between now and six months from now; paying down debt, making investments in your home or business, saving for retirement by investing in interest-bearing instruments like stocks, bonds, mutual funds, etc. There's absolutely no advantage and every disadvantage to waiting 6 months to receive the same amount of money that you could get now. However, if I gave you a choice between $1000 now and $1100 in six months, that might be a harder question; you will get more money later, so the question becomes, how much can you improve your net worth in six months given $1000 now? If it's more than $100, you still want the money now, but if nothing you can do will make more than $100, or if there is a high element of risk to what you can do that will make $100 that might in fact cause you to lose money, then you might take the increased, guaranteed money later. There are two fundamental formulas used to calculate the time value of money; the ""future value"" and the ""present value"" formulas. They're basically the same formula, rearranged to solve for different values. The future value formula answers the question, ""how much money will I have if I invest a certain amount now, at a given rate of return, for a specified time""?. The formula is FV = PV * (1+R)N, where FV is the future value (how much you'll have later), PV is the present value (how much you'll have now), R is the periodic rate of return (the percentage that your money will grow in each unit period of time, say a month or a year), and N is the number of unit periods of time in the overall time span. Now, you asked what ""compounding"" is. The theory is very simple; if you put an amount of money (the ""principal"") into an investment that pays you a rate of return (interest), and don't touch the account (in effect reinvesting the interest you earn in the account back into the same account), then after the first period during which interest is calculated and paid, you'll earn interest on not just the original principal, but the amount of interest already earned. This allows your future value to grow faster than if you were paid ""simple interest"", where interest is only ever paid on the principal (for instance, if you withdrew the amount of interest you earned each time it was paid). That's accounted for in the future value formula using the exponent term; if you're earning 8% a year on your investment, then after 1 year you'll have 108% of your original investment, then after two years you'll have 1.082 = 116.64% (instead of just 116% which you'd get with simple interest). That .64% advantage to compounding doesn't sound like much of an advantage, but stay tuned; after ten years you'll have 215.89% (instead of 180%) of your original investment, after 20 you'll have 466.10% (instead of 260%) and after 30 your money will have grown by over 1000% as opposed to a measly 340% you'd get with simple interest. The present value formula is based on the same fundamental formula, but it's ""solved"" for the PV term and assumes you'll know the FV amount. The present value formula answers questions like ""how much money would I have to invest now in order to have X dollars at a specific future time?"". That formula is PV = FV / (1+R)N where all the terms mean the same thing, except that R in this form is typically called the ""discount rate"", because its purpose here is to lower (discount) a future amount of money to show what it's worth to you now. Now, the discount rate (or yield rate) used in these calculations isn't always the actual yield rate that the investment promises or has been shown to have over time. Investors will calculate the discount rate for a stock or other investment based on the risks they see in the company's financial numbers or in the market as a whole. The models used by professional investors to quantify risk are rather complex (the people who come up with them for the big investment banks are called ""quants"", and the typical quant graduates with an advanced math degree and is hired out of college with a six-figure salary), but it's typically enough for the average investor to understand that there is an inherent risk in any investment, and the longer the time period, the higher the chance that something bad will happen that reduces the return on your investment. This is why the 30-year Treasury note carries a higher interest rate than the 10-year T-note, which carries higher interest than the 6-month, 1-year and 5-year T-bills. In most cases, you as an individual investor (or even an institutional investor like a hedge fund manager for an investment bank) cannot control the rate of return on an investment. The actual yield is determined by the market as a whole, in the form of people buying and selling the investments at a price that, coupled with the investment's payouts, determines the yield. The risk/return numbers are instead used to make a ""buy/don't buy"" decision on a particular investment. If the amount of risk you foresee in an investment would require you to be earning 10% to justify it, but in fact the investment only pays 6%, then don't buy it. If however, you'd be willing to accept 4% on the same investment given your perceived level of risk, then you should buy." I don't like REITs because they are more closely correlated to the movement of the stock market. They don't really do the job of diversifying a portfolio because of that correlation.  When the stock market dropped in 2008, REITs were hammered as well because the housing bubble burst. Bonds went up, and if you rebalanced (sold the bonds to buy more stock) then you came out much further ahead when the stock market recovered. The point of adding bonds for diversification is that they move in the opposite direction of equities; blunting the major drops (and providing buying opportunities). REITs don't fit that bill. REITs are not undergoing a correction like bonds because the price of real estate is a function of housing supply and buyer demand. Rising interest rates only make it a little harder for buyers to buy, so the effect of rising interest rates on real estate prices is muted. The other effects on real estate prices (more wealth in the economy for buyers) pushes in the opposite direction of the rising interest rates. A stock is an ownership interest in a company.  There can be multiple classes of shares, but to simplify, assuming only one class of shares, a company issues some number of shares, let's say 1,000,000 shares and you can buy shares of the company. If you own 1,000 shares in this example, you would own one one-thousandth of the company.  Public companies have their shares traded on the open market and the price varies as demand for the stock comes and goes relative to people willing to sell their shares. You typically buy stock in a company because you believe the company is going to prosper into the future and thus the value of its stock should rise in the open market. A bond is an indebted interest in a company.  A company issues bonds to borrow money at an interest rate specified in the bond issuance and makes periodic payments of principal and interest.  You buy bonds in a company to lend the company money at an interest rate specified in the bond because you believe the company will be able to repay the debt per the terms of the bond.  The value of a bond as traded on the open exchange varies as the prevailing interest rates vary.  If you buy a bond for $1,000 yielding 5% interest and interest rates go up to 10%, the value of your bond in the open market goes down so that the payment terms of 5% on $1,000 matches hypothetical terms of 10% on a lesser principal amount.  Whatever lesser principal amount at the new rate would lead to the same payment terms determines the new market value.   Alternatively, if interest rates go down, the current value of your bond increases on the open market to make it appear as if it is yielding a lower rate. Regardless of the market value, the company continues to pay interest on the original debt per its terms, so you can always hold onto a bond and get the original promised interest as long as the company does not go bankrupt. So in summary, bonds tend to be a safer investment that offers less potential return.  However, this is not always the case, since if interest rates skyrocket, your bond's value will plummet, although you could just hold onto them and get the low rate originally promised. "The rate of the bond is fixed. But there is a risk known as ""interest rate risk"". Basically, if you have a 2 percent bond and market rates are 4 percent, you'll have to offer your bond at a discount or nobody would buy it. So if you ever needed to sell it, you'd lose a bit of money." Okay let's try this a different way. Completely forget about what the bond is with. Here is how a bond works:   * You get paid interest for holding the bond (5% interest means a coupon of $50 assuming one coupon a year)    * At the end of the bond term (maturity) you get paid $1000.     In your scenario, you get paid the $50 as an interest payment and the $1000 final payment.    If you only had the bond for one year, your total payment will be $1050.     Try drawing a timeline to visualise it a bit better "Thanks!  Do you know how to calculate the coefficients from this part?:  ""The difference between the one-year rate and the spread coefficients represents the response to a change in the one-year rate. As a result, the coefficient on the one-year rate and the difference in the coefficients on the one-year rate and spread should be positive if community banks, on average, are asset sensitive and negative if they are liability sensitive. The coefficient on the spread should be positive because an increase in long-term rates should increase net interest income for both asset-sensitive and liability-sensitive banks.""  The one-year treasury yield is 1.38% and the ten-year rate is 2.30%.  I would greatly appreciate it if you have the time!" The duration of a bond tells you the sensitivity of its price to its yield. There are various ways of defining it (see here for example), and it would have been preferable to have a more precise statement of the type of duration we should assume in answering this question. However, my best guess (given that the duration is stated without units) is that this is a modified duration. This is defined as the percentage decrease in the bond price for a 1% increase in the yield. So, change in price = -price x duration (as %) x change in yield (in %) For your duration of 5, this means that the bond price decreases by a relative 5% for every 1% absolute increase in its yield. Using the actual yield change in your question, 0.18%, we find: change in price = -1015 x 5% x (4.87 - 4.69) = -9.135 So the new price will be 1015 - 9.135 = £1005.865