Bond investers often like to buy shares in mutual funds that give returns that closely follow commonly quoted indices, such as the Lehman Brothers Government Index. One popular index is computed from several thousand different bond types.

(a) Roughly how many bonds do you think would be needed in a portfolio that could reliably give one year portfolio returns within half a percentage point of the index?

You can assume bond returns typically vary in range from -5% to +5% with a standard deviation of about 2.5%, but state any other assumptions you make for this.