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Lessons
One short lesson for each skill in the Learn room. Read it, try the numbers, then answer three questions that count toward your mastery.
In 1880 Van Gogh taught himself to draw by copying the sheets of Charles Bargue’s drawing books one at a time; “now I’ve finished the 60 sheets,” he wrote to Theo that September. These lessons are plates in the same spirit: each is short, works an example step by step, and ends with you doing it yourself.
Start here
Plate 1: Time value and discounted cash flow
A dollar today is worth more than a dollar next year. Discounting puts every future cash flow into today’s money, and a DCF adds them up.
19 lessons · progress is kept in this browser
Finance
- Time value and discounted cash flowA dollar today is worth more than a dollar next year. Discounting puts every future cash flow into today’s money, and a DCF adds them up.
- The cost of capitalInvestors lend and invest only if they expect a return. The cost of capital is that expected return, and it is the rate a DCF discounts at.
- Choosing between projectsNPV, IRR, payback and the profitability index often agree. When they don’t, NPV is the one to trust, and knowing why is most of capital budgeting.
- Bonds, yields and durationA bond’s price is its fixed payments discounted at today’s yield. Duration says how far that price moves when yields do.
- Return, risk and diversificationA share is judged by the return it earns for the risk it carries. Combining shares that don’t move together cuts risk faster than it cuts return.
- Options and what drives their valueAn option is a right without an obligation. Its value comes from what the share might do before expiry, which is why volatility matters so much.
- Value at Risk and Expected ShortfallValue at Risk is the loss a portfolio should exceed only rarely. Expected Shortfall asks how bad those rare days are, and a backtest asks whether the model was right.
- Spotting financial distressFive ratios from the accounts, weighted into one score, separated manufacturers that went bankrupt from those that didn’t. Altman’s Z-score is still the standard first screen.
Business analytics
- Describing data: centre, spread and correlationBefore any model, describe the data: where its middle is, how far it spreads, and which columns move together. Each summary can mislead in a known way.
- Regression: what the coefficients and R² sayA regression line turns “these move together” into “this much more of y for each unit of x”. Its numbers come with uncertainty, and the diagnostics say when to doubt them.
- Classification: odds, thresholds and the confusion matrixA churn model gives each customer a probability. Turning that into a decision means choosing a threshold, and every threshold trades missed churners against false alarms.
- Supervised learning: comparing models fairlyFour models can answer the same yes-or-no question. The fair way to pick one is to score each only on rows it never trained on, and to know what each model is doing.
- Unsupervised learning: groups and directionsWith no outcome to predict, the question becomes: which rows are alike, and which few directions carry most of the variation? Clustering answers the first; principal components the second.
- Seasonal forecasting with Holt-WintersA seasonal series has a level, a trend and a pattern that repeats every year. Holt-Winters tracks all three, updating each as new figures arrive, and a fair test tells you whether to trust it.
Marketing
- Price elasticity and the best priceHow much do sales fall when the price rises? Elasticity answers in percentages, and with the cost of a unit it points to the price that earns the most.
- Segmentation and targetingSplit a market into groups that want different things, describe each group against the average customer, and choose the one you can serve best.
- Choosing markets: attractiveness and reachRank countries on what makes a market worth entering, on one scale and with weights you choose, then weigh how attractive each is against how hard it is to reach.
- Unit economics and experimentsIs each customer worth more than it costs to win? Lifetime value against acquisition cost, how fast that cost comes back, and how to read a test of a new idea.
How I build the models
How the lessons work
A worked example first
Beginners who study worked examples before solving problems learn faster and make fewer errors on similar problems than those who start by solving (Sweller and Cooper, 1985).
Then you try
Each lesson’s calculator lets you change the inputs and see the answer move, the step from following an example to using the idea.
Then you’re tested
Retrieving an idea strengthens memory more than rereading it (Roediger and Karpicke, 2006), and a large review rates practice testing and spaced practice the most useful study techniques (Dunlosky et al., 2013). The questions update your mastery, and Practise brings the skill back before you forget it.
Short pieces
Lessons are split into small labelled parts, without decoration, so working memory goes on the idea (Mayer, 2009).
Sources
- Van Gogh to Theo van Gogh, Cuesmes, 7 September 1880, letter 157.
- Sweller, J. & Cooper, G. A. (1985). The use of worked examples as a substitute for problem solving in learning algebra. Cognition and Instruction, 2(1), 59–89.
- Roediger, H. L. & Karpicke, J. D. (2006). Test-enhanced learning: taking memory tests improves long-term retention. Psychological Science, 17(3), 249–255.
- Dunlosky, J., Rawson, K. A., Marsh, E. J., Nathan, M. J. & Willingham, D. T. (2013). Improving students’ learning with effective learning techniques. Psychological Science in the Public Interest, 14(1), 4–58.
- Mayer, R. E. (2009). Multimedia Learning (2nd ed.). Cambridge University Press.