The rolling down the yield curve strategy delivers the highest relative returns when the curve is upward sloping. This is because:

• Rolling down the yield curve involves buying bonds with maturities longer than the investment horizon
• As time passes, the bond's remaining maturity decreases, and it "rolls down" to lower yields on the curve
• The steeper the upward slope, the greater the yield decline as the bond moves down the curve
• This yield decline translates into price appreciation, generating additional returns beyond the coupon income

With a flat or downward sloping curve, there is little or no yield advantage to be gained from this strategy.