Lesson 5 of 7

Risk: drawdown, volatility, diversification, position sizing, and cash

Learning goal

Compute a drawdown, explain volatility and diversification, size positions by inverse volatility, and see how cash protects a fund.

Explanation

Risk is the chance of a result you cannot accept. The client's risk is a deep fall. So the challenge measures falls directly.

Drawdown is the fall from a previous high. Maximum drawdown (MDD) is the deepest such fall across the whole test.

Drawdown = (peak − low) / peak

Losses are harder to recover than they look. A 25% fall needs a 33.3% gain to get back. A 50% fall needs 100%.

Volatility is how much returns swing from week to week. A calm industry has low volatility. A jumpy one has high volatility. The challenge measures it as the sample standard deviation of the last 26 weekly returns, with a floor of 0.1% a week.

Diversification means holding assets that do not all fall together. When one lags, another may help. The result is a smoother ride. It does not remove risk.

Position sizing decides how much to put in each holding. Two methods are available:

Equal weight: each holding gets the same share.
Inverse volatility: calmer industries get more, jumpier ones get less. Each holding's weight is proportional to 1 divided by its volatility. The challenge measures volatility over the last 26 weeks.

Cash is a holding too. It earns the Treasury bill rate and does not fall in a crash. Holding cash gives up growth to buy safety.

Worked example

Drawdown. Fund values by week: 100, 110, 125, 100, 90, 105, 118, 130.

The running peak reaches 125 in week 3.
The lowest value after it is 90.
Drawdown = (125 − 90) / 125 = 35 / 125 = 28%.
After week 8, the value 130 is a new high, so the old drawdown ends. The MDD of this fund is 28%.

For this client, 28% breaks the limit of 25%. To recover from 90 to 125 needs a gain of 125 / 90 − 1 = 38.9%.

Inverse volatility with two industries. Industry A swings about 1% a week. Industry B swings about 3%.

Inverse values: 1/1 = 1.000 and 1/3 = 0.333.
Total: 1.333.
Weight A = 1.000 / 1.333 = 75%. Weight B = 0.333 / 1.333 = 25%.

The calm industry gets three times the weight of the jumpy one.

Diversification. Industry X returns +20% then −10%. Industry Y returns −10% then +20%. Held alone, X gives 1.20 × 0.90 = 1.08. Split 50/50 (each period): 1.05 × 1.05 = 1.1025. The mix ends higher and moves less.

Cash and the regime rule. K = 3, equal weight: each industry is 33.3%. The market falls below its average and Y = 50%. Each industry is scaled to 16.7%. Total in industries: 50%. Cash: 50%. If industries then fell 40%, the loss on that half is about 20% of the fund, before the small interest on cash. With no regime rule, the same fall would cost about 40%.

What this means in the challenge

Block 4, position sizing: Equal or Inverse volatility. Block 3 sets how much goes to cash when the market weakens. Fewer holdings (small K) mean more concentrated risk. A hurdle that moves weight to cash lowers risk too.

The client's limit is a fall of no more than a quarter (25%). You are scored on risk in three ways:

Excess return per drawdown = (fund CAGR − cash CAGR) / max(MDD, 5%). Growth beyond cash earned per unit of pain. A fund that sits in cash scores zero. Example: CAGR 9%, cash CAGR 3%, MDD 20% gives (9 − 3) / 20 = 0.30.
Relative drawdown = your MDD / max(market MDD, 5%). Lower is better. A value of 0.5 means your fund fell half as far as the market. If your fund was invested less than 50% of the time on average in a window, that window counts as 1.0.
Mandate kept: 6 points if your median MDD across the hidden windows is 25% or less.

Time invested (the average total industry weight) tells you how much of the time you were out of the market. A fund that sits in cash can look safe but may grow too little.

In the final's stress room you face one 26-week crisis. Think now about where your own rules are weak, because Part 3 question 2 asks which market scenario hurts your sealed fund most. The right answer is the scenario with the lowest total return for your fund, and any scenario within 1 percentage point of it also scores.

Self-check

Fund values: 100, 120, 90, 108. What is the maximum drawdown? Does it meet the client's limit?
Show the answer
Answer: The peak is 120. The low after it is 90. (120 − 90) / 120 = 30 / 120 = 25%. The client's limit is "no fall of more than a quarter," and a fall of exactly 25% is not more than a quarter. It meets the limit, with no margin to spare. (The platform's mandate test is also "25% or less.")
Industry A has volatility 2% and industry B has 4%. What are the inverse-volatility weights?
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Answer: Inverse values: 1/2 = 0.50 and 1/4 = 0.25. Total 0.75. A = 0.50 / 0.75 = 66.7%. B = 0.25 / 0.75 = 33.3%.
K = 3, equal weight, the regime rule is triggered with Y = 25%. What weight does each industry hold, and how much is cash?
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Answer: Each industry: 33.3% × 25% = 8.3%. Total in industries: 25%. Cash: 75%.