Lesson 4 of 7
Relative strength and momentum
Learning goal
Calculate an N-week return, rank ten industries, apply a hurdle, and explain why last period's leaders can fall behind.
Explanation
Momentum is the tendency of recent winners to keep winning for a while. It is not a law. It is a tendency, and it fails often.
To measure it, use an N-week return, also called the lookback:
N-week return = (index now / index N weeks ago) − 1
Relative strength compares one asset to another, usually to the market. If an industry rose 18% and the market rose 6%, the industry beat the market. Divide the industry index by the market index and watch that ratio. When the ratio rises, the industry is outperforming.
The challenge uses ten US industry groups. You rank them from best N-week return to worst. You hold the top K. Ranking by N-week return gives the same order as ranking by relative strength against the market. Dividing every industry by the same market number does not change the order.
A hurdle is a test a chosen industry must pass. Allowed hurdles: None, Must beat the market, or Must have a positive return. An industry that fails has its share moved to cash.
Why leaders flip. Industries lead because of news, fashion, or the business cycle. These change. A short lookback (4 weeks) reacts fast but follows noise. A long lookback (52 weeks) is steady but turns late. No lookback fits every period.
Rebalancing is the schedule on which you refresh your choices. With a rebalance every R weeks, the decision weeks are weeks 0, R, 2R, and so on. Between those weeks, the fund holds its target weights and does not change them (apart from stops and the regime rule). Each change costs 0.10% of the size of the change in each industry's weight.
Worked example
Ten industries, 26-week returns (made up). Market: +6%.
| Rank | Industry | 26-week return |
|---|---|---|
| 1 | Technology | +18% |
| 2 | Healthcare | +12% |
| 3 | Consumer Staples | +9% |
| 4 | Retail & Services | +7% |
| 5 | Manufacturing | +5% |
| 6 | Utilities | +3% |
| 7 | Telecom & Media | +1% |
| 8 | Other incl. Finance | −2% |
| 9 | Energy | −6% |
| 10 | Consumer Durables | −9% |
- K = 3, hurdle None. Hold Technology, Healthcare, Consumer Staples at 1/3 each.
- K = 5, equal weight, hurdle "Must beat the market". The top five get 20% each. Manufacturing (+5%) is below the market (+6%). It fails. Its 20% goes to cash. The fund holds 80% in four industries and 20% in cash.
- K = 5, hurdle "Must have a positive return". All five are positive. All pass. Nothing moves to cash.
Same order by relative strength: Technology 1.18 / 1.06 = 1.113, Healthcare 1.12 / 1.06 = 1.057, Consumer Staples 1.09 / 1.06 = 1.028. The ratios are in the same order as the returns.
Rebalance schedule with R = 8: weeks 0, 8, 16, 24. With R = 4: weeks 0, 4, 8, 12.
Ties in ranking are broken by a fixed order: Consumer Staples, Consumer Durables, Manufacturing, Energy, Technology, Telecom & Media, Retail & Services, Healthcare, Utilities, Other.
Self-check
An industry index moves from 80 to 92 over N weeks. What is the N-week return?
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Answer: 92 / 80 − 1 = 0.15, so +15%.
K = 2, equal weight, hurdle "Must beat the market." The market returned +10%. The top two industries returned +14% and +8%. What does the fund hold?
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Answer: The top industry (+14%) beats the market (+10%) and passes. The second (+8%) fails. Each had a base weight of 50%. The fund holds 50% in the top industry and 50% in cash.
List the rebalance weeks up to week 13 for R = 4. Then give one reason the best industry today may not be the best next quarter.
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Answer: Rebalance weeks: 0, 4, 8, 12. Reason: leadership changes with news, fashion, or the business cycle. A strong recent return does not guarantee the next one. A short lookback may also have followed noise.