The Problem

• It is only May of our first year now.

• Not enough data, not enough data on factors.

Data Problems

• We do not have three years of monthly data on which to evaluate our strategy. We only have about 4 months.

  • We cannot help this.

  • Our means (averages) suck as estimates of true performance. There is little we can do.

  • Our variances suck, but less so.

    • we can (always) improve our estimate of variances and covariances by working with daily returns rather than monthly returns.

Factor Problems

• We do not have daily real-time data on the French factor portfolios.

  • We will use Vanguard portfolio as stand-ins for other factor portfolios.

  • We can download them in real time.

  • Attribution relative to Vanguard factors is in itself interesting, too.

  • The attribution method is always the same

Attribution

• If we had invested in factor (=portfolio) X instead, how much would we have made?

• How loaded/related are we to factor X?

• What part of our portfolio is “due to” our loading on factor X?

Shame?

• Both your and the factor portfolio can have alpha with respect to other models, such as the CAPM.

• It is no shame to have lower alphas when more factors are included. You are really working out how similar your portfolio is.

  • you may not want to tell clients that they can get your alpha elsewhere, though.

  • but you may also be on the buyer’s side.

Minimum: 3+ Benchmark Models

Try different factor models (on the RHS), at least

• a 0-factor (relative to risk-free rate),

• a 1-factor (relative to CAPM),

• a more general factor portfolio.

Identity

If r_p − r_f = a + b_p1 ⋅ (f₁) + c_p2 ⋅ (f₂) + ϵ_p then μ(r_p−r_f) = a + b_p1 ⋅ μ(f₁) + c_p2 ⋅ μ(f₂) + μ(ϵ_p) where μ(x) means the average of x.

• The regression fitting sets μ(ϵ_p) to zero.

• The first factor should always be r_m − r_f.

Attribute Contribution

• The attribute contribution is each term in the sum (beta times mean), which will add up to your portfolio return.

• This works with more factors, too.

• All factors (here, f₁ and f₂) should be zero investment pfios, just like your r_p − r_f.

  • If we use a long-only portfolio as the basis of a factor f, then subtract r_f, too.

  • Use daily returns!

Example

Is your portfolio performance due to loading on a particular industry? Use industry funds.

Where to get industry funds? Search!

Examples:

• https://personal.vanguard.com/us/FundsLargeSector.

• https://etfdb.com/etfs/issuers/vanguard/

Same For Everyone

Our four-factor benchmark.

• VOO (S&P500) - RF, where RF is not yield but return!

• VTV (Value) - VUG (Growth)

• VIG (Dividends) - VOO (S&P500)

• VV (Large-Cap) - VBR (Small-Cap)

PS: always show 0-factor and 1-factor models, too.

Heterogeneity

• In the real world, different funds use different benchmarks and attributions.

• We entertain two versions. A collective version where everyone uses the same factors, and your own.

Do some more “choice” attribution

• Pick your own factors and tell us where your performance comes from.

• For example, VGT (Info Tech) - RF could be one…or energy, or….