Absolute risk, measured by sigma, is reduced if you add a security that has low correlation with the rest of your portfolio, which leads to better diversification.
Active risk, measured by tracking error (or s.d. of active returns), is reduced if you add a security that has a high correlation with the benchmark returns. This is because now your actively managed portfolio has one more asset that kind of mimics the benchmark.
Looks good to me. Now to further your understanding, pretend this is an exam question…
Manager A, who manages a fund benchmarked to S&P 500, would like to increase cash holdings. How does that impact the fund’s Absolute Risk and how does that impact the fund’s Active risk. Circle One (Increase, decrease, or no impact) and justify.
Decrease
Increase
Zero marks out of 6. You did not circle, and you failed to justify!
I can already hear my parents when I tell them I fail.
Decrease since it would have low correlation with S&P500.
Not sure…stays the same or increase?
I circle Decrease for the absolute risk as cash is riskless and you will earn the Risk free rate if you hold cash.
I circle increase for active risk as cash held has low risk relative to any other holding in the benchmark leading to a higher active risk since adding cash will significantly decrease portfolio risk relative to benchmark, increasing active risk.
How much would you give me out of 6, sire ?
Regarding item 2, believe if you’re holding cash (say for defensive purposes) in a portfolio that is replicating S&P500 then this should generate higher tracking error since the cash holdings are considered as an “off benchmark” holding and the standard deviation of the difference in returns between the portfolio and index would increase.
A. Decrease - Increasing cash would decrease the absolute risk (standard deviation of portfolio returns) in the portfolio. Adding cash reduces portfolio volatility, and thus absolute risk.
B. Increase - Increasing cash increases active risk (tracking error, or standard deviation of portfolio returns minus benchmark return). This is because as more cash is added, the more the actively managed portfolio deviates from the benchmark portfolio. However, if the benchmark portfolio also has a certain % of cash, altering the active portfolio cash position to match that in the benchmark portfolio may reduce active risk.
Maybe a 5. You didn’t relate why absolute risk would decrease. You just gave the definition of cash and said it is riskless. You correctly identified active risk would decrease because of the low relative risk with holdings.
Looks good. Although the second part of B sounds more like active share than active risk. Just deviating from the position is active share, while deviating from the risk is active risk… but you correctly stated it in terms of tracking error in the earlier sentence.
+6 (i hope I saw circles and not ovals)
You guys could be way more succinct in my opinion - how is active risk calculated? it’s the standard deviation of active return.
With more cash in the portfolio - active return widens (on an absolute basis), wider active return = wider active risk.
Or, if you’re crunched for time, I’d have just writed “Duh”.