How to calculate the price of a bond based with a yield to Maturity, term and annual interest?
"Like all financial investments, the value of a bond is the present value of expected future cash flows.  The Yield to Maturity is the annualized return you get on your initial investment, which is equivalent to the discount rate you'd use to discount future cash flows. So if you discount all future cashflows at 6% annually*, you can calculate the price of the bond: So the price of a $1,000 bond (which is how bond prices are typically quoted) would be $1,097.12. The current yield is just the current coupon payment divided by the current price, which is 70/1,097.12 or 6.38% Question 3 makes no sense, since the yield to maturity would be the same if you bought the bond at market price Question 4 talks about a ""sale"" date which makes me think that it assumes you sold the bond on the coupon date, but you'd have to know the sale price to calculate the rate of return." "The answer to almost all questions of this type is to draw a diagram.  This will show you in graphical fashion the timing of all payments out and payments received.  Then, if all these payments are brought to the same date and set equal to each other (using the desired rate of return), the equation to be solved is generated. In this case, taking the start of the bond's life as the point of reference, the various amounts are: Pay out = X Received = a series of 15 annual payments of $70, the first coming in 1 year.  This can be brought to the reference date using the formula for the present value of an ordinary annuity. PLUS Received = A single payment of $1000, made 15 years in the future.  This can be brought to the reference date using the simple interest formula. Set the pay-out equal to the present value of the payments received and solve for X I am unaware of the difference, if any, between ""current rate"" and ""rate to maturity"" Finding the rate for such a series of payments would start out the same as above, but solving the resulting equation for the interest rate would be a daunting task..."
"In general, yes. If interest rates go higher, then any existing fixed-rate bonds - and hence ETFs holding those bonds - become less valuable. The further each bond is from maturity, the larger the impact. As you suggest, once the bonds do mature, the fund can replace them at a market price, so the effect tails off. The bond market has a concept known as ""duration"" that helps reason about this effect. Roughly, it measures the average time from now to each payout of the bond, weighted by the payout. The longer the duration, the more the price will change for a given change in interest rates. The concept is just an approximation, and there are various slightly different ways of calculating it; but very roughly the price of a bond will reduce by a percentage equal to the duration times the increase in interest rates. So a bond with a duration of 5 years will lose 5% of its value for a 1% rise in interest rates (and of course vice-versa). For your second question, it really depends on what you're trying to achieve by diversifying - this might be best as a different question that gives more detail, as it's not very related to your first question. Short-term bonds are less risky. But both will lose value if the underlying company is in trouble. Gilts (government bonds) are less risky than corporate bonds." 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. "1. Interest rates What you should know is that the longer the ""term"" of a bond fund, the more it will be affected by interest rates. So a short-term bond fund will not be subject to large gains or losses due to rate changes, an intermediate-term bond fund will be subject to moderate gains or losses, and a long-term bond fund will be subject to the largest gains or losses. When a book or financial planner says to buy ""bonds"" with no other qualification, they almost always mean investment-grade intermediate-term bond funds (or for individual bonds, the equivalent would be a bond ladder averaging an intermediate term). If you want technical details, look at the ""average duration"" or ""average maturity"" of the bond fund; as a rough guide, if the duration is 10, then a 1% change in interest rates would be a 10% gain or loss on the fund. Another thing you can do is look at long-term (10 years or ideally longer) performance history on some short, intermediate, and long term bond index funds, and you can see how the long term funds bounced around more. Non-investment-grade bonds (aka junk bonds or high yield bonds) are more affected by factors other than interest rates, including some of the same factors (economic booms or recessions) that affect stocks. As a result, they aren't as good for diversifying a portfolio that otherwise consists of stocks. (Having stocks, investment grade bonds, and also a little bit in high-yield bonds can add diversification, though. Just don't replace your bond allocation with high-yield bonds.) A variety of ""complicated"" bonds exist (convertible bonds are an example) and these are tough to analyze. There are also ""floating rate"" bonds (bank loan funds), these have minimal interest rate sensitivity because the rate goes up to offset rate rises. These funds still have credit risks, in the credit crisis some of them lost a lot of money. 2. Diversification The purpose of diversification is risk control. Your non-bond funds will outperform in many years, but in other years (say the -37% S&P 500 drop in 2008) they may not. You will not know in advance which year you'll get. You get risk control in at least a few ways. There's also an academic Modern Portfolio Theory explanation for why you should diversify among risky assets (aka stocks), something like: for a given desired risk/return ratio, it's better to leverage up a diverse portfolio than to use a non-diverse portfolio, because risk that can be eliminated through diversification is not compensated by increased returns. The theory also goes that you should choose your diversification between risk assets and the risk-free asset according to your risk tolerance (i.e. select the highest return with tolerable risk). See http://en.wikipedia.org/wiki/Modern_portfolio_theory for excruciating detail. The translation of the MPT stuff to practical steps is typically, put as much in stock index funds as you can tolerate over your time horizon, and put the rest in (intermediate-term investment-grade) bond index funds. That's probably what your planner is asking you to do. My personal view, which is not the standard view, is that you should take as much risk as you need to take, not as much as you think you can tolerate: http://blog.ometer.com/2010/11/10/take-risks-in-life-for-savings-choose-a-balanced-fund/ But almost everyone else will say to do the 80/20 if you have decades to retirement and feel you can tolerate the risk, so my view that 60/40 is the max desirable allocation to stocks is not mainstream. Your planner's 80/20 advice is the standard advice. Before doing 100% stocks I'd give you at least a couple cautions: See also:" "A mutual fund's return or yield has nothing to do with what you receive from the mutual fund. The annual percentage return is simply the percentage increase (or decrease!) of the value of one share of the mutual fund from January 1 till December 31. The cash value of any distributions (dividend income, short-term capital gains,  long-term capital gains) might be reported separately or might be included in the annual return.  What you receive from the mutual fund is the distributions which you have the option of taking in cash (and spending on whatever you like, or investing elsewhere) or of re-investing into the fund without ever actually touching the money. Regardless of whether you take a distribution as cash or re-invest it in the mutual fund, that amount is taxable income in most jurisdictions. In the US, long-term capital gains are taxed at different (lower) rates than ordinary income, and I believe that long-term capital gains from mutual funds are not taxed at all in India. You are not taxed on the increase in the value of your investment caused by an increase in the share price over the year nor do you get deduct the ""loss"" if the share price declined over the year. It is only when you sell the mutual fund shares (back to the mutual fund company) that you have to pay taxes on the capital gains (if you sold for a higher price) or deduct the capital loss (if you sold for a lower price) than the purchase price of the shares. Be aware that different shares in the sale might have different purchase prices because they were bought at different times, and thus have different gains and losses.  So, how do you calculate your personal return from the mutual fund investment? If you have a money management program or a spreadsheet program, it can calculate your return for you. If you have online access to your mutual fund account on its website, it will most likely have a tool called something like ""Personal rate of return"" and this will provide you with the same calculations without your having to type in all the data by hand. Finally, If you want to do it personally by hand, I am sure that someone will soon post an answer writing out the gory details." Perfect super clear, thank you /u/xlct2  So it is like you buy a bond for $X, start getting interest, sell bond for $X :)  I was thinking there could be a possibility of a bond working like a loan from a bank, that you going paying as time goes by :D Simple math. Take the sale proceeds (after trade expenses) and divide by cost. Subtract 1, and this is your return. For example, buy at 80, sell at 100, 100/80 = 1.25, your return is 25%. To annualize this return, multiply by 365 over the days you were in that stock. If the above stock were held for 3 months, you would have an annualized return of 100%.  There's an alternative way to annualize, in the same example above take the days invested and dive into 365, here you get 4. I suggested that 25% x 4 = 100%. Others will ask why I don't say 1.25^4 = 2.44 so the return is 144%/yr. (in other words, compound the return, 1.25x1.25x...) A single day trade, noon to noon the next day returning just 1%, would multiply to 365% over a year, ignoring the fact there are about 250 trading days. But 1.01^365 is 37.78 or a 3678% return. For long periods, the compounding makes sense of course, the 8%/yr I hope to see should double my money in 9 years, not 12, but taking the short term trades and compounding creates odd results of little value. "A (very) simplified bond-pricing equation goes thus: Fair_Price: {Face_Value * (1 + Interest - Expected_Market_Return) ^ (Years_To_Maturity)} * P(Company_Will_Default_Before_Maturity) To reiterate, that is a very simplified model. But it allows us to demonstrate the 3 key factors that drive ""Fair"" Value: The interest relative to the current market rate. If your AAA bond yields 1%, but an equally-good AAA bond currently sells at 3% in the market, then the ""Equivalent"" value is the face value minus 2% (1% - 3%) for every year to maturity.  Years to maturity. Because 1) is multiplied for every year to maturity, longer-dated bonds are more sensitive to changes in market rates. If your bond yields 2% less than market but matures in a year, then it's worth $98, but if it matures in 56 years, then it's only worth 0.98^56 = $32. Conversely, if your bond yields more than the market rate, then its' price will be greater than face value. The company might default on the debt. If a Bond has a ""Fair"" Value of $100, but you think there's a 50% chance that the company will default, then it's only worth $50. In fact, it can be worth even less because getting paid on a defaulted bond can often take time and/or money and/or lawyers. In your case, because your bond matures in 56 years but yields ~5% (well above the current market rate), for it to be below Face value implies a strong probability of default, or a strong belief that market returns will be above 5% over the next 56 years." "Below I will try to explain two most common Binomial Option Pricing Models (BOPM) used. First of all, BOPM splits time to expiry into N equal sub-periods and assumes that in each period the underlying security price may rise or fall by a known proportion, so the value of an option in any sub-period is a function of its possible values in the following sub period. Therefore the current value of an option is found by working backwards from expiry date through sub-periods to current time. There is not enough information in the question from your textbook so we may assume that what you are asked to do is to find a value of a call option using just a Single Period BOPM. Here are two ways of doing this: First of all let's summarize your information: Current Share Price (Vs) = $70 Strike or exercise price (X) = $60 Risk-free rate (r) = 5.5% or 0.055 Time to maturity (t) = 12 months Downward movement in share price for the period (d) = $65 / $70 = 0.928571429 Upward movement in share price for the period (u) = 1/d = 1/0.928571429 = 1.076923077 ""u"" can be translated to $ multiplying by Vs => 1.076923077 * $70 = $75.38 which is the maximum probable share price in 12 months time. If you need more clarification here - the minimum and maximum future share prices are calculated from stocks past volatility which is a measure of risk. But because your textbook question does not seem to be asking this - you probably don't have to bother too much about it yet. Intrinsic Value: Just in case someone reading this is unclear - the Value of an option on maturity is the difference between the exercise (strike) price and the value of a share at the time of the option maturity. This is also called an intrinsic value.  Note that American Option can be exercised prior to it's maturity in this case the intrinsic value it simply the diference between strike price and the underlying share price at the time of an exercise. But the Value of an option at period 0 (also called option price) is a price you would normally pay in order to buy it. So, say, with a strike of $60 and Share Price of $70 the intrinsic value is $10, whereas if Share Price was $50 the intrinsic value would be $0. The option price or the value of a call option in both cases would be fixed.  So we also need to find intrinsic option values when price falls to the lowest probable and rises to the maximum probable (Vcd and Vcu respectively) (Vcd) = $65-$60 = $5 (remember if Strike was $70 then Vcd would be $0 because nobody would exercise an option that is out of the money) (Vcu) = $75.38-$60 = $15.38 1. Setting up a hedge ratio:  h = Vs*(u-d)/(Vcu-Vcd) h = 70*(1.076923077-0.928571429)/(15.38-5) = 1 That means we have to write (sell) 1 option for each share purchased in order to hedge the risks. You can make a simple calculation to check this, but I'm not going to go into too much detail here as the equestion is not about hedging. Because this position is risk-free in equilibrium it should pay a risk-free rate (5.5%). Then, the formula to price an option (Vc) using the hedging approach is: (Vs-hVc)(e^(rt))=(Vsu-hVcu) Where (Vc) is the value of the call option, (h) is the hedge ratio, (Vs) - Current Share Price, (Vsu) - highest probable share price, (r) - risk-free rate, (t) - time in years, (Vcu) - value of a call option on maturity at the highest probable share price. Therefore solving for (Vc): (70-1*Vc)(e^(0.055*(12/12))) = (75.38-1*15.38) => (70-Vc)*1.056540615 = 60 => 70-Vc = 60/1.056540615 => Vc = 70 - (60/1.056540615)  Which is similar to the formula given in your textbook, so I must assume that using 1+r would be simply a very close approximation of the formula above. Then it is easy to find that Vc = 13.2108911402 ~ $13.21 2. Risk-neutral valuation: Another way to calculate (Vc) is using a risk-neutral approach. We first introduce a variable (p) which is a risk-neutral probability of an increase in share price. p = (e^(r*t)-d)/(u-d) so in your case: p = (1.056540615-0.928571429)/(1.076923077-0.928571429) = 0.862607107 Therefore using (p) the (Vc) would be equal: Vc = [pVcu+(1-p)Vcd]/(e^(rt)) => Vc = [(0.862607107*15.38)+(0.137392893*5)]/1.056540615 => Vc = 13.2071229185 ~ $13.21 As you can see it is very close to the hedging approach. I hope this answers your questions. Also bear in mind that there is much more to the option pricing than this. The most important topics to cover are: Multi-period BOPM Accounting for Dividends Black-Scholes-Merton Option Pricing Model"