investment strategies and shit Flashcards
A passive investment strategy
assumes that market prices of securities are fairly priced
who tries to maintain an appropriate risk exposure OR simply replicate the return of the market (Bond market index)
Passive managers
Immunization
type of passive investment strategy that tries to hedge a portfolio against interest rate risk
what creates interest rate risk
the sensitivities of bonds’ prices to interest rates’
An active investment strategy
tries to achieve abnormal returns (returns in excess of the risk taken)
two ways to achieve an active investment strategy
Relying on interest rates (IR) forecasts to predict bond movements
Looking for mispriced bonds
bond market risk
Bond prices fluctuate as interest rates fluctuate
This up or down movement in the prices of bonds creates a risk that bonds’ investors have to face
Bond pricing relationships (properties)
- Bond prices and yields are inversely related
–> As yields increase, bond prices fall and vice versa
- An increase in bond’s yield to maturity results in a smaller price change than a decrease in yield of equal magnitude.
- Prices of long-term bonds tend to be more sensitive to IR changes than prices of short-term bonds
–> Cash flows are discounted at higher rates)+
- The sensitivity of bond prices to changes in yields increases at a decreasing rate as maturity increases
–> IR risk is less than proportional to bond maturity
- IR risk is inversely related to the bond’s coupon rate
–> Prices of low coupon bonds are more sensitive to changes in IR than prices of high coupon bonds
- The sensitivity of a bond’s price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling.
why do Zero-coupon bonds have a well-defined time to maturity?
no payments until maturity
how do Coupon paying bonds apply Effective Maturity?
Average of all the maturities of all promised cash flows
Duration or (Macaulay Duration)
a measure that proxies the sensitivity of a bond to interest rate risk
–> The higher the bond’s duration, the higher the sensitivity of the bond to interest rate risk
approximates the sensitivity of the bond to interest rate risk
Price change is proportional to duration
duration of a coupon paying bond
the weighted average of the time to receive all payments (each coupon and principal payment made by the bond)
D = E(t · wt)
wt = (CFt / (1 + y)^t) / bond price
duration of a zero-coupon bond
its time to maturity
the modified duration
to estimate bond’s price movements relative to movements in bond’s YTM
D* = D / (1 + y)
The percentage change in bond’s price relative to changes in the bond’s YTM formula using the modified duration
(Delta P) / P = -D*(Delta y)
Bond’s Duration is affected by which three major factors?
Bond’s time to maturity
Bond’s coupon rate
Bond’s yield to maturity
Duration has the which four major properties?
- The duration of a zero coupon bond is equal to its maturity
- Holding maturity constant, a bond’s duration is higher when the coupon rate is lower
- Holding coupon rate constant, a bond’s duration generally increases with bond’s maturity.
–> Duration always increases for bonds selling at par and at a premium
–> Duration does not always increase for bonds selling at a discount!
- Holding other factors constant, the duration of coupon bond is higher when the bond’s YTM is lower
The duration of a perpetuity (infinitely lived bond) is equal to
D = (1 + y) / y
the bond convexity
it shows how bond prices change (decrease) as a interest rates change (increase)
–> it shows that it is not a linear function
–> the higher the interest rates, the less prices will drop the more interest rates rise
–> the lower the interest rates, the more prices will drop the more interest rates rise
the rate of change of the slope of the price-yield curve,
expressed as a fraction of the bond price
The higher the convexity of the bond, the higher the curvature in the price-yield curve
convexity formula
(1 / (P · (1 + y)^2)) · E((CFt/(1 + y)^t) · (t^2 + t))
Convexity correction
allows us improve the duration approximation
why is convexity desired by investors
because it increases the price of bonds whether YTM increases or decreases
–> If the bond convexity is positive, then the second term of its formula is positive as well and it will add to the price of the bond whether interest rates increase or decrease
–> If interest rates increase, the price of a bond with larger convexity will decrease less than that with lower convexity
–> If interest rates decrease, the price of a bond with larger convexity will increase more than that with lower convexity
which two classes of passive bond management are generally taken by investors?
Indexing strategy
Immunization strategy
Indexing strategy
attempts to replicate the performance of a given bond index
An index bond portfolio would have the same risk-reward profile as the index to which it is tied
Immunization strategy
attempts to protect the firm from the exposure to interest rates fluctuations
An immunized bond portfolio would have almost zero market risk; in the sense that any fluctuations in interest rates would not affect the bond portfolio value
Several challenges facing bond index portfolio formation
bond indices include very large number of bonds (around 5,000 in the US)
many bonds are thinly traded (especially in Canada)
–> fair market pricing is difficult
Bonds generate continuous income (the coupons) that need to be invested
Frequent rebalancing of their bond portfolios to accommodate the changes in the constituents of the bond index:
–> • Bonds are dropped from the index as their maturity is less than one year
–> • New bonds are issued need to be added to index
is it feasible to precisely replicate a bond index?
if not, what do we do instead
nah bruv
A stratified sampling approach is followed by bond investors instead
A stratified sampling approach
They only hold a representative sample of the bonds in the actual index
- Divide the universe of bonds into several categories:
–> Maturity
–> Issuer Credit
–> Risk Coupon rate
- Each category is further divided in several divisions
–> Any bond should be associated with one division of every category
–> Subdivisions are formed containing the pool of bonds associated with them
–> Bonds falling within each subdivision are considered homogeneous
- Estimate the percentage of the whole bonds universe falling within each subcategory
- Establish a bond portfolio by selecting few bonds from each subcategory on condition that you keep the percentage weights of each category in your portfolio similar to that of the index
explain the mismatch between the maturity of asset and liabilities for banks?
what then happens if interest rates rise unexpectedly?
Banks have short term liabilities and long term assets
If IR rise unexpectedly then Bank suffers serious decrease in net worth since
–> Assets fall in value by more than the liabilities
explain the Pension funds’ mismatch between IR sensitivity of assets held in the fund and the PV of its liabilities
how do they do their immunization?
As IR drop the value of liabilities grow even faster than the value of their assets
–> objective is to make value of assets track the value of liabilities if IR increase or decrease
Liabilities of Pensions is long-dated meaning they need to match assets duration to liabilities duration
–> They invest in alternative assets with long durations like real-estate and infrastructure
basically, they get a bond at a certain interest rate so that the future values of cashflows and the future PV of the sale of the bond equal the long term liabilities
–> if interest rate decreases, the future value of cashflows decrease, but the future value of the sale of the bond will increase offsetting the former effect
–> if interest rate increases, the future value of cashflows increase, offsetting the future value of the sale of the bond decreasing
–> in the end, wether an increase or decrease, they can still pay their long term debts
we make sure we hold the bond until we owe our debts
more effective in small changes in interest rates
Immunization protect investors against which two types of risks?
Price risk
Reinvestment rate risk
Once index bond managers immunize a portfolio, why do portfolio managers have to rebalance the portfolio?
As time goes on, interest rates change leading to new duration for both assets and liabilities
–> These need to be re-matched
As time goes on, the duration of assets and liabilities changes
–> This triggers a rebalancing to re-match both assets duration and liabilities duration
true or false
once a duration based immunization is adopted, the net worth of the portfolio is protected from interest rate risk at that point in time only
true
Time passage and other factors affect the durations of assets and liabilities and a manager must rebalance the portfolio fixed-income assets continuously to realign its duration with the duration of the obligations
Without rebalancing, the durations will become unmatched and the immunization’s objective is not reached
why is continuous rebalancing is not feasible?
It requires continuous resources
It costs a lot due to transaction costs
–> as a result, a compromise is usually adopted to balance between the accuracy of the immunization techniques and the rebalancing costs
—-> Chose imperfect immunization over trading costs
a Dedication Strategy
Cash Flow Matching on a multi-period basis
to match a series of obligations to a selection of either zero-coupon or coupon bonds
it eliminates the need for rebalancing
not always possible to do
why is it not always possible to do Cash Flow Matching?
If we are facing perpetual obligation (like retirees of pension funds), we cannot find zero-coupon bonds with hundreds of years of maturities
–> It would be infeasible
Duration based immunization
relies on duration estimates
–> strictly valid only for a flat yield curve
–> where all payments are discounted at a common IR
—-> not always correct as spot rates vary
do we need to consider inflation in immunization strategies?
yeee
the two possible sources of potential profit for active bond managers?
Proper forecasting of the interest rates fluctuations
Successful identification of mispriced fixed income securities
Homer and Liebowitz identified which four types of bond swaps that bond portfolio managers follow in their attempt to actively manage a portfolio?
The substitution Swap
The Intermarket Spread Swap
The Rate Anticipation Swap
The Pure Yield Pickup Swap
the two possible sources of potential profit for active bond managers?
Proper forecasting of the interest rates fluctuations
Successful identification of mispriced fixed income securities
–> A positive abnormal return based on such strategies is highly linked to the accuracy of the managers’ information or insights
Homer and Liebowitz identified which four types of bond swaps that bond portfolio managers follow in their attempt to actively manage a portfolio?
The substitution Swap
The Intermarket Spread Swap
The Rate Anticipation Swap
The Pure Yield Pickup Swap
The Substitution Swap
an investor swaps one bond with another having the same characteristics (equal coupon, maturity, quality, and other possible features) because these bonds have non-justified differences in prices
Such a swap would be motivated by a belief that the discrepancy between the bonds is a mispricing and it represents a profit opportunity
The Intermarket Spread Swap
In an intermarket swap an investor swaps, for example, one 20 year government with another 20 year Baa corporate bond
would be motivated by a belief that the yield spread (difference between the yields) between two sectors of bonds is temporarily out of line
The Rate Anticipation Swap
an investor swaps bonds with longer duration with
those of shorter duration and vice versa
motivated by an anticipated increase (decrease) in interest rates
–> if interest rates are expected to decrease, an investor will swap the short term two government bonds with the longer term 20 years government bonds
–> The latter have higher duration and will have a greater increase in their prices than the short term one
The Pure Yield Pickup Swap
an investor swaps a bond with higher YTM with
one having a lower YTM
motivated by the assumption that interest rates will not move during the life of the swap
–> An investor in this swap is ready to bear the interest rate risk
