Valuation of financial assets, tutored in English
An asset valuation tutor for students on English-taught finance modules in Spain. Bond pricing and duration, share valuation, portfolio theory, CAPM and an introduction to derivatives, one to one and online whenever suits you.
This module is where finance stops being descriptive and starts being quantitative, and that transition catches people out. The formulas look intimidating, but nearly all of them are the same idea repeated: work out the cash flows, decide the right discount rate, bring them to today. Once you see that, the syllabus shrinks.
Bond valuation, yield and the price-yield relationship
Pricing a bond is discounting its coupons and its redemption value at the yield the market demands. From there come the properties the exam wants you to explain: why a bond trades above par when the coupon beats the yield and below par when it does not, what happens to the price as maturity approaches, and how yield to maturity differs from the current yield and from the coupon rate. We work with annual and semi-annual coupons, and with zero-coupon bonds where the whole return is in the redemption.
Duration, modified duration and convexity
Duration measures how long you wait, on average, for a bond's cash flows, weighting each date by the present value of the flow arriving then. Modified duration turns that into a sensitivity: the approximate percentage price change for a one point move in yield. We calculate both by hand, and then look at why the estimate is always slightly pessimistic on the downside. That gap is convexity, and understanding it is usually worth a mark or two in the written part.
Share valuation and the dividend discount model
Valuing equity as the present value of expected dividends. The constant growth or Gordon model, when it applies and, more importantly, when it breaks, which is whenever the growth rate approaches the required return. Multi-stage models where high growth fades to a sustainable rate. We also cover the relationship between retention, growth and return, and the multiples approach, so you can comment on why a market price and your model disagree.
Risk, return and portfolio theory
Expected return and standard deviation for a single asset, then covariance and correlation for two, and why combining assets that do not move together lowers risk without necessarily lowering return. We build the efficient frontier, add a risk-free asset to get the capital market line, and separate diversifiable risk from the systematic risk you cannot avoid. This is the conceptual spine of the module and everything after it assumes you have it.
CAPM, beta and the cost of equity
The capital asset pricing model states that required return equals the risk-free rate plus beta times the market risk premium. We work on where beta comes from, how to interpret a beta above or below one, how to calculate a portfolio beta, and what the security market line tells you about an asset that plots off it. We also look honestly at the model's limitations, because exam questions increasingly ask for a critique rather than just a number.
An introduction to derivatives
Forwards and futures, how a forward price is set by arbitrage, and how margin works. Then options: calls and puts, intrinsic and time value, payoff diagrams at expiry, put-call parity and the intuition behind binomial pricing. We keep the treatment at the level your module needs rather than going into stochastic calculus, unless your syllabus genuinely goes there.
Where almost everyone gets stuck
Discounting at the coupon rate instead of the yield
The coupon rate tells you how much cash the bond pays. The yield tells you what the market demands to hold it. They are only equal when the bond trades at par. Using the coupon as the discount rate always returns a price of exactly par, which should be your warning sign that something has gone wrong.
Applying the Gordon model when growth exceeds the required return
The constant growth model needs the growth rate to be below the required return. If it is not, the denominator turns negative and you get a negative share price, which is not an answer. It is a signal that constant growth is the wrong assumption and you need a multi-stage model instead.
Confusing total risk with systematic risk
Standard deviation measures total risk. Beta measures only the part that moves with the market. A share can be very volatile and still have a low beta if its volatility is company-specific. CAPM prices beta, not standard deviation, because the rest can be diversified away, and exams test whether you know the difference.
Worked example: price, duration and sensitivity of a three-year bond
A bond has a face value of 1,000 euros, pays an annual coupon of 5% and has 3 years to maturity. The yield required by the market is 6%. Calculate the price of the bond, its Macaulay duration and its modified duration. Then estimate how far the price would fall if the yield rose to 7%, and compare that estimate with the exact price at 7%.
- Cash flows and price. You receive 50 euros at t=1, 50 at t=2 and 1,050 at t=3 (coupon plus face value). Discounting at 6%: 50/1.06 = 47.17; 50/1.06^2 = 44.50; 1,050/1.06^3 = 881.60. Price = 47.17 + 44.50 + 881.60 = 973.27 euros. It trades below par because the yield (6%) is above the coupon (5%).
- Macaulay duration. Weight each period by the present value of its cash flow: (1 x 47.17) + (2 x 44.50) + (3 x 881.60) = 47.17 + 89.00 + 2,644.80 = 2,780.97. Divide by the price: 2,780.97 / 973.27 = 2.8573 years.
- Modified duration. D_mod = 2.8573 / (1 + 0.06) = 2.6956. Read it as: if the yield rises by 100 basis points, the price falls by roughly 2.6956%.
- Estimating the fall. Change in price is approximately -2.6956% x 973.27 = -26.24 euros. Estimated price at 7% = 973.27 - 26.24 = 947.03 euros.
- Exact check at 7%. 50/1.07 = 46.73; 50/1.07^2 = 43.67; 1,050/1.07^3 = 857.11. Actual price = 947.51 euros. The duration estimate was 0.48 euros too low: that gap is convexity, which is why duration always overstates a price fall.
SolutionPrice at 6% = 973.27 euros. Macaulay duration = 2.8573 years. Modified duration = 2.6956. For a rise in yield from 6% to 7%, the estimated fall is 26.24 euros (estimated price 947.03) against an actual price of 947.51; the 0.48 euro difference is convexity.
About these lessons in particular
My module is called Investments or Financial Markets. Is this the same content?
Usually yes. Bond and share valuation, portfolio theory, CAPM and derivatives appear under several module names. Send me your syllabus and I will tell you what overlaps before you commit to anything.
Do you cover the Excel side as well?
Yes, if your course assesses it. We can build the valuation and the portfolio calculations in a spreadsheet, though I will always make you do the first one by hand so you know what the function is computing.
Are the lessons in English or Spanish?
Whichever you prefer, and you can change your mind mid-lesson. I live and study in the United States, so working through valuation in English is completely natural for me.
I also teach
Shall we work on it together?
Tell me where you are, which university you are at and when the exam is. I will get back to you as soon as I can.