Constructing a Fixed Income Portfolio

When first constructing a portfolio, there is a whole host of questions that the fund manager must consider. The answer they give to these questions will determine the efficiency of their investment strategy. 

What proportion of cash, bonds, and equities should be held?

What is the appropriate risk vs reward balance that we should aim for?

How many assets are required to reap diversification benefits?

Should we invest in domestic or foreign assets? Should they be hedged?

What is the time horizon of our investment? How much liquidity is required?

How should the weightings of the assets held be determined?

Which sectors should we invest in? Corporate or government?

How often should adjustments be made to the portfolio holdings?

This post will seek to answer the above questions and in the process develop a strategy for the construction of a fixed income portfolio for a hypothetical client. Since our client is at retirement age, they have requested a portfolio entirely composed of fixed income assets. Investing in government bonds would certainly be a minimal risk strategy, however to better match the risk profile of the client it has been decided to invest instead in corporate bonds. Relative to equities bonds yield returns with much lower volatility so such a portfolio will naturally be low risk. The risk tolerance of the investor was measured as slightly-below average, but not extremely low. For this reason, 90 per cent of the portfolio will be comprised of investment grade bonds (rated BBB+ or greater) and 10 per cent of the portfolio will be comprised of high yield bonds (BBB or lower). 

The next decision to make is how many assets to hold within the portfolio. Dbouk & Kryzanowski (2010) examine the diversification benefits associated with different-sized portfolios of bonds using various metrics. They examine the marginal diversification gains by industry sector, credit ratings, and maturity. In general, they find that the optimal portfolio size is about 40 bonds with associated diversification benefits of about 80%. For this reason the portfolio will be constructed by selecting 40 different corporate bonds.

Research by Liu (2012) investigates whether US investors can achieve diversification benefits by adding international corporate bonds to their portfolio. His findings show that such an approach can significantly reduce portfolio volatility and increase Sharpe ratio, reducing risk by as much as 82.4 per cent. Based on these findings the portfolio to be constructed will be diversified among British, American, Australian, Canadian, European, and Japanese corporate bonds. The bonds purchased will be issued in foreign currency, and as such appropriate currency hedges will be employed (to be discussed further in a later post).

Next, we must consider the appropriate time horizon of our investment portfolio and the liquidity requirements of the client. The client has indicated that they may require access to some portion of the funds after 5 years. For this reason, at least half of the bonds selected for the portfolio will have maturities of approximately 5 years. 

The weighting strategy of the portfolio will follow a simple 1/N strategy, whereby equal allocation values are maintained for each asset. While this simple portfolio strategy does not optimize with respect to any return information, it is easy to implement and not subject to any bias.  DeMiguel, Garlappi, and Uppal (2009) show that across a large class of sample based mean variance portfolio allocation models, no model consistently out performs the 1/N naive portfolio allocation strategy in out of sample performance. 

Finally, it is worth considering the industry sectors chosen for investment. The focus of the diversification strategy employed so far is primarily geographical with some consideration given to choosing bonds of different maturities. As such, sector diversification has been deemed of lesser importance. However, where possible bonds from a range of different sectors have been selected for each country. 

The portfolio was constructed using the PRTU function in Bloomberg.

Here is a breakdown of the bonds chosen by country, maturity, and industry:

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Risk Tolerance and Capacity for Loss

The Financial Services Authority (FSA) is responsible for the regulation of financial services in the UK. In 2011, the FSA released a guidance paper on suitable investment selection procedures for independent financial advisers. The paper called for advisers to distinguish clearly between the risk preferences and risk capacity. 

The FSA defines capacity for loss as "the customer’s ability to absorb falls in the value of their investment", and suggests that "if any loss of capital would have a materially detrimental effect on their standard of living, this should be taken into account in assessing the risk that they are able to take". In contrast risk tolerance (or alternatively attitude to risk) can be defined as "the maximum amount of uncertainty that someone is willing to accept when making a financial decision" (Grable, 2000). Clearly, the distinction between the two measures is that capacity for loss measures how much risk the investor is able to take whereas attitude to risk aims to measure how much risk the investor is willing to take. 

The two aspects of risk are best illustrated through an example. Below is a description of a hypothetical investor who wishes to invest £1,000,000 in a fixed income portfolio:

The client is a male 55 year old semi-retired doctor. He co-owns his own practice, with his share valued at £320,000. He currently works a 4 day week, earning £90,000 per annum, but expects to be cutting down his hours further in the years to come. He has a wife and three adult children, with only one of the children still living at home. Their house is valued at £300,000 and the combined value of their two cars is £80,000. His wife is a retired academic, but she occasionally volunteers at local universities as a guest lecturer. The investor would like to know that his funds are reasonably secure and will provide primarily income with some element of capital appreciation. At present the client does not envisage requiring access to their funds for at least 5 years but they may reserve the right to re-visit this. When he retires fully, in perhaps 5 to 10 years time, the client plans on selling his share of the medical practice and buying a medium sized luxury yacht.

From the above description the factors which likely affect the client's attitude to risk and capacity for loss can be distinguished:

Factors affecting attitude to risk Male Retirement age Married Highly educated High income, currently £90,000 / yr Respected occupation

Factors affecting capacity for loss Income stream for the next 5-10 yrs Value of investment: £1,000,000 Value of assets: £700,000 Expected future expenses (yacht) High living standard to maintain High social status to maintain

Research suggests that males are more risk tolerant than females, as are those with higher attained education, higher income, greater financial knowledge and more professional occupations (Grable, 2000). Age also plays a significant role, and it is generally accepted that risk tolerance decreases with age. Hallahan, Faff, & McKenzie (2004) found that psychometric Risk Tolerance Scores (RTS) decrease non-linearly with age, as shown in the figure below: 

This highlights how an investor's risk preferences may change with time and may need to be reassessed as they progress towards later stages of life. The hypothetical client described above is 55 years old, and therefore would look for greater security in his investment portfolio despite the other factors which may otherwise indicate a very high risk profile.

To best tailor the portfolio to the client's requirements a valid and reliable estimate of their risk tolerance level is required. One such tool is the Grable and Lytton (1999) Risk Tolerance Scale. Provided below is the risk tolerance quiz used by Grable and Lytton, which you can use to estimate your own risk tolerance profile. How does it compare with the score of the 55 year old doctor below? What might be the reasons for these differences?

Risk Tolerance estimate for the client: (22) = Below-average risk tolerance

Investment Risk Tolerance Quiz (Grable and Lytton, 1999)

1. In general, how would your best friend describe you as a risk taker?

(1)  A real risk avoider

(2)  Cautious 

(3)  Willing to take risks after completing adequate research

(4)  A real gambler

2. You are on a TV game show and can choose one of the following. Which would you take?

(1)  $1,000 in cash

(2)  A 50% chance at winning $5,000

(3)  A 25% chance at winning $10,000

(4)  A 5% chance at winning $100,000

3. You have just finished saving for a "once-in-a-lifetime" vacation. Three weeks before you plan to leave, you lose your job. You would:

(1)  Cancel the vacation

(2)  Take a much more modest vacation

(3)  Go as scheduled, reasoning that you need the time to prepare for a job search

(4)  Extend your vacation, because this might be your last chance to go first-class

4. If you unexpectedly received $20,000 to invest, what would you do?

(1)  Deposit it in a bank account, money market account, or an insured CD

(2)  Invest it in safe high quality bonds or bond mutual funds

(3)  Invest it in stocks or stock mutual funds

5. In terms of experience, how comfortable are you investing in stocks or stock mutual funds?

(1)  Not at all comfortable 

(2)  Somewhat comfortable 

(3)  Very comfortable

6. When you think of the word "risk" which of the following words comes to mind first?

(1)  Loss 

(2)  Uncertainty 

(3)  Opportunity 

(4)  Thrill

7. Some experts are predicting prices of assets such as gold, jewels, collectibles, and real estate (hard assets) to increase in value; bond prices may fall, however, experts tend to agree that government bonds are relatively safe. Most of your investment assets are now in high-interest government bonds. What would you do?

(1)  Hold the bonds 

(2)  Sell the bonds, put half the proceeds into money market accounts, and the other half into hard assets 

(3)  Sell the bonds and put the total proceeds into hard assets 

(4)  Sell the bonds, put all the money into hard assets, and borrow additional money to buy more

8. Given the best- and worst-case returns of the four investment choices below, which would you prefer?

(1)  $200 gain best case; $0 gain/loss worst case 

(2)  $800 gain best case; $200 loss worst case 

(3)  $2,600 gain best case; $800 loss worst case 

(4)  $4,800 gain best case; $2,400 loss worst case

9. In addition to whatever you own, you have been given $1,000. You are now asked to choose between:

(1)  A sure gain of $500 

(2)  A 50% chance to gain $1,000 and a 50% chance to gain nothing

10. In addition to whatever you own, you have been given $2,000. You are now asked to choose between:

(1)  A sure loss of $500 

(2)  A 50% chance to lose $1,000 and a 50% chance to lose nothing

11. Suppose a relative left you an inheritance of $100,000, stipulating in the will that you invest ALL the money in ONE of the following choices. Which one would you select?

(1)  A savings account or money market mutual fund 

(2)  A mutual fund that owns stocks and bonds 

(3)  A portfolio of 15 common stocks 

(4)  Commodities like gold, silver, and oil

12. If you had to invest $20,000, which of the following investment choices would you find most appealing?

(1)  60% in low-risk investments 30% in medium-risk investments 10% in high-risk investments 

(2)  30% in low-risk investments 40% in medium-risk investments 30% in high-risk investments 

(3)  10% in low-risk investments 40% in medium-risk investments 50% in high-risk investments

13. Your trusted friend and neighbor, an experienced geologist, is putting together a group of investors to fund an exploratory gold mining venture. The venture could pay back 50 to 100 times the investment if successful. If the mine is a bust, the entire investment is worthless. Your friend estimates the chance of success is only 20%. If you had the money, how much would you invest?

(1)  Nothing 

(2)  One month's salary 

(3)  Three month's salary 

(4)  Six month's salary

Add up all of the blue numbers for each of your responses. In general, the score that you receive can be interpreted as follows:

(18) or below = Low risk tolerance

(19) to (22) = Below-average risk tolerance

(23) to (28) = Average/moderate risk tolerance

(29) to (32) = Above-average risk tolerance
(33) and above = High risk tolerance

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