Singer-Terhaar and adding securities to portfolios mkt, notice, should

Iginla2010

Anyone else notice that these are basically the same thing?

RP(asset class) = Std Dev(asset class) * Corr * sharpe ratio(mkt)

or

RP(asset class) / std dev(asset class) = Corr * sharpe ratio(mkt)
which is:
sharpe ratio(asset class) = Corr * sharpe ratio(mkt)

So basically:
Singer-Terhaar says that the SR of the asset class should equal the mkt SR times the correlation b/w the two.
In the context of asset class selection if the asset class SR is greater than portfolio SR * correlation b/w the two you should add it to the portfolio